SNF_presentation.ipynb

{
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   "source": [
    "# Fysik, statistik och lite artificiell intelligens <br/>- en bild av den moderna ingenjören\n",
    "## Christian Forssén"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Teoretisk subatomär fysik, Institutionen för fysik, Chalmers\n",
    "\n",
    "#### 2018-01-18, SNF Cocktail party\n",
    "* Denna presentation är baserad på en [ipython](https://ipython.org/) notebook. Själva presentationen är en [Reveal.js](https://revealjs.com/#/) HTML slideshow skapad genom [nbconvert](https://github.com/jupyter/nbconvert) direkt från ovan nämnda notebook.\n",
    "* Allt material och källkod är samlat i säkert men publikt [git](https://git-scm.com/) förvar (ett s.k. \"git repository\") på [github](https://github.com/cforssen/SNFcocktail), tillgängligt för alla och envar att ladda ner och testa själv.\n",
    "```\n",
    "[~]$ git clone https://github.com/cforssen/SNFcocktail.git\n",
    "[~]$ cd SNFcocktail\n",
    "```\n",
    "* Se också [Teoretisk subatomär fysiks](http://fy.chalmers.se/subatom/tsp/index.php) hemsida (se [\"for students\"](http://fy.chalmers.se/subatom/tsp/index.php?page=teaching))."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "## Innehåll\n",
    "* Först lite fysik\n",
    "* ... och lite statistik i två olika skepnader\n",
    "* ... plus lite beräkningsfysik\n",
    "* Sedan en ny horisont genom att kombinera fysik och statistik med maskininlärning\n",
    "* ... och slutligen framträder en bild av den moderna ingenjören!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "## Att kvantifiera sin osäkerhet är inte lätt..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "> Ett militärt angrepp mot Sverige är osannolikt.\n",
    "\n",
    "Stefan Löfvén, 2018."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "> Ett väpnat angrepp på Sverige kan inte uteslutas.\n",
    "\n",
    "Försvarsberedningen, 2017."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Inom naturvetenskap är kunskap om osäkerheter av stor betydelse."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "#### Referenser\n",
    "* Intressant och lärorik bloggpost [\"Frequentism and Bayesianism: A Practical Introduction\"](http://jakevdp.github.io/blog/2014/03/11/frequentism-and-bayesianism-a-practical-intro/) på bloggen [Pythonic Perambulations](http://jakevdp.github.io).\n",
    "* Litteratur: [Data Analysis: A Bayesian Tutorial](https://global.oup.com/academic/product/data-analysis-9780198568322?cc=se&lang=en&) och [Bayesian Logical Data Analysis for the Physical Sciences](https://www.cambridge.org/core/books/bayesian-logical-data-analysis-for-the-physical-sciences/09E9A95DAE275F5B005676C71B542598)\n",
    "* [GPy](http://sheffieldml.github.io/GPy/) en pythonmodul för Gaussprocesser (GP), från maskininlärningsgruppen på Sheffield University.\n",
    "* [TensorFlow](https://www.tensorflow.org/) ett öppet programbibliotek för maskinintelligens genom neurala nätverk. Det utgör basen för [Keras](https://keras.io/): ett python API för Deep Learning.\n",
    "* ... för min del började detta med ett 26-dimensionellt optimeringsproblem inom utvecklandet av effektiva fältteorier, en gedigen statistisk analys (samt några mycket hängivna kandidatarbetare och en väldigt duktig doktorand): [Phys. Rev. X 6 (2016) 011019](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.011019)."
   ]
  },
  {
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   "source": [
    "## Python\n",
    "\n",
    "Att installera Python, samt de bibliotek som möjliggör vetenskapliga beräkningar, är inte särskilt svårt.\n",
    "\n",
    "Jag rekommenderar Anaconda, med pakethanteraren conda, som fungerar för Windows, Linux, och Mac OS X.\n",
    "\n",
    "- [Anaconda](https://www.continuum.io/downloads) inkluderar både Python och conda, samt ett antal förinstallerade paket. Denna distribution tar dock en hel del plats. Ett alternativ är [Miniconda](http://conda.pydata.org/miniconda.html). Se också [condas online dokumentation](http://conda.pydata.org/docs/)\n",
    "\n",
    "Välj en version med Python 3–och installera de moduler som krävs för denna presentation:\n",
    "\n",
    "```\n",
    "[~]$ conda install numpy scipy pandas gpy matplotlib seaborn jupyter\n",
    "```\n",
    "\n",
    "Eller ännu bättre, skapa en virtuell miljö för just detta projekt (alla nödvändiga moduler listas i filen 'environment.yml'):\n",
    "```\n",
    "[~]$ conda env create\n",
    "[~]$ source activate SNF-env\n",
    "```"
   ]
  },
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   "metadata": {
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   "source": [
    "Sedan startar vi en [jupyter (ipython) notebook](http://jupyter.org/):\n",
    "```\n",
    "[~]$ jupyter notebook SNF_presentation.ipynb\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "och börjar med att importera ett par viktiga moduler:"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {
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     "slide_type": "-"
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   "source": [
    "# Some care is needed when removing warnings. But for the final version of this notebook it should be safe.\n",
    "import warnings\n",
    "warnings.simplefilter(\"ignore\", UserWarning)\n",
    "warnings.simplefilter(\"ignore\", FutureWarning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   },
   "outputs": [],
   "source": [
    "# Not really needed, but nicer plots\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "sns.set_context(\"talk\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "# Subatomär fysik \n",
    "## från det lilla till det stora"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Theoretical Subatomic Physics](http://fy.chalmers.se/subatom/tsp/index.php), Department of Physics, Chalmers\n",
    "\n",
    "![](figures/800px-tsp.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "### Subatomär fysik är fundamentalt gränsöverskridande\n",
    "| Vetenskapsfält | Längdskala\t    | Exempel på vetenskapliga frågor |\n",
    "|---------------|-------------|-------------|\n",
    "| Astrofysik och kosmologi | giga | -Hur har våra grundämnen bildats i universum? <br/>-Vad är mörk materia? |\n",
    "| Kvantfenomen | nano | -Hur uppstår kollektiva fenomen ur system med många partiklar? <br/>-Vilka unika egenskaper har öppna kvantsystem? |\n",
    "| Kärnfysik   | femto | -Vilka isotoper är bundna? <br/>-Kan atomkärnor användas för precisionstester av fundamentala symmetrier? |\n",
    "| Partikelfysik | subfemto | -Kan vi lösa QCD för hadroniska system? <br/>-Hur skulle en ny standardmodell för partikelfysik kunna konstrueras? |"
   ]
  },
  {
   "cell_type": "markdown",
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    }
   },
   "source": [
    "# Effektiva teorier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
    }
   },
   "source": [
    "Användbart för att beskriva okänd fysik i termer av effektiva frihetsgrader och kända observationer:\n",
    "* T.ex. atomkärnor i termer av protoner och neutroner trots att de underliggande frihetsgraderna är kvarkar och gluoner.\n",
    "* Eller växelverkan mellan mörk materia och vanlig materia trots att vi inte vet vad för partikel det är eller hur själva växelverkan förmedlas.\n",
    "\n",
    "Kräver dock vetskap om relevanta skalor och symmetrier."
   ]
  },
  {
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   },
   "source": [
    "## Svag växelverkan enligt Fermi (1933)\n",
    "\n",
    "![](figures/200px-svag_vxv_utan_W.png)"
   ]
  },
  {
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   "source": [
    "och idag enligt Standardmodellen\n",
    "\n",
    "![](figures/278px-svag_vxv_med_W.png)"
   ]
  },
  {
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   "source": [
    "En klassisk analogi till en effektiv teori är multipolexpansion av ett elektriskt fält långt bort från en okänd (men liten) laddningsfördelning ($a \\ll r$).\n",
    "\n",
    "![](figures/charge_distribution.png)\n",
    "\n",
    "Dvs hur kan vi beskriva den elektriska potentialen som en summa av mindre och mindre viktiga termer (vi inför en dimensionslös expansionsparameter $\\frac{a}{r} \\ll 1$) samt ett begränsat antal okända parametrar $c_i$ (att jämföra med den stora mängd information som finns inbyggd i total kunskap om laddningsfördelningen):\n",
    "\n",
    "$$\n",
    "\\phi(\\vec{r}) = c_0 \\left( \\frac{a}{r} \\right)^0 + c_1 \\left( \\frac{a}{r} \\right)^1 + c_2 \\left( \\frac{a}{r} \\right)^2 + \\ldots\n",
    "$$"
   ]
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   },
   "source": [
    "Det visar sig (se detaljer nedan...) att\n",
    "\n",
    "$$\n",
    "\\phi(\\vec{r}) \\propto \\frac{q}{r} \\left[ 1 + \\tilde{\\mu}(\\theta) \\left( \\frac{a}{r} \\right)^1 + \\tilde{Q}(\\theta) \\left( \\frac{a}{r} \\right)^2 + \\mathcal{O}\\left( \\frac{a^3}{r^3} \\right) \\right]\n",
    "$$\n",
    "\n",
    "där \n",
    "* $q$ är den totala laddningen hos laddningsfördelningen,\n",
    "* $\\tilde{\\mu}(\\theta)$ är dess (dimensionslösa) dipolmoment,\n",
    "* $\\tilde{Q}(\\theta)$ är dess (dimensionslösa) kvadrupolmoment,\n",
    "* etc"
   ]
  },
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     "slide_type": "skip"
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   },
   "source": [
    "Lite mer detaljer.\n",
    "$$\n",
    "\\phi(\\vec{r}) \\propto \\int \\frac{\\rho(\\vec{r}')}{|\\vec{r} - \\vec{r}'|} dV'\n",
    "= \\frac{1}{r} \\left[ \\int \\rho(\\vec{r}') dV' + \\int \\rho(\\vec{r}') \\frac{r'}{r} \\cos\\theta dV' \n",
    "+ \\int \\rho(\\vec{r}') \\left(\\frac{r'}{r}\\right)^2 \\left( \\frac{3}{2}\\cos^2\\theta - \\frac{1}{2}\\right) dV' + \\ldots \n",
    "\\right]\n",
    "= \\frac{q}{r} \\left[ \\left( \\frac{a}{r} \\right)^0 + \\tilde{\\mu} \\left( \\frac{a}{r} \\right)^1 + \\tilde{Q} \\left( \\frac{a}{r} \\right)^2 + \\mathcal{O}\\left( \\frac{a^3}{r^3} \\right) \\right]\n",
    "$$"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "där vi har använt att\n",
    "$$\n",
    "\\frac{1}{|\\vec{r} - \\vec{r}'|} = \\frac{1}{r} \\times \\frac{1}{|\\hat{r} - \\hat{r}'(r'/r)}\n",
    "= \\frac{1}{r} \\times \\frac{1}{[1 -2\\cos\\theta(r'/r)+(r'/r)^2]^{1/2}}\n",
    "$$\n",
    "och gjort en Taylorutveckling ($r'/r \\ll 1$)\n",
    "$$\n",
    "\\frac{1}{|\\vec{r} - \\vec{r}'|} = \\frac{1}{r} \\left[ 1 + \\cos\\theta \\left( \\frac{r'}{r} \\right) + \\left( \\frac{3}{2}\\cos^2\\theta - \\frac{1}{2} \\right) \\left( \\frac{r'}{r} \\right)^2 + \\mathcal{O} \\left( \\frac{r'^3}{r^3} \\right) \\right]\n",
    "$$\n",
    "Den totala laddningen ges uppenbart av integralen\n",
    "$$\n",
    "q = \\int \\rho(\\vec{r}') dV'\n",
    "$$\n",
    "medan de andra multipolmomenten ges av liknande integraler som uppkommer genom de följande termerna i Taylorutvecklingen."
   ]
  },
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   },
   "source": [
    "## Kvantstegen\n",
    "\n",
    "![](figures/kvantstegen_800x478.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "> Du kan välja vilka frihetsgrader som du vill för att beskriva ett fysikaliskt system.\n",
    "> Men väljer du fel så kommer du att ångra dig.\n",
    "\n",
    "S. Weinberg (fritt översatt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "subslide"
    }
   },
   "source": [
    "## Starkt växelverkande system\n",
    "För att beskriva stark växelverkan vid låga energier är det (nästan) praktiskt omöjligt att använda QCD med kvarkar och gluoner som frihetsgrader. \n",
    "\n",
    "Istället har man utvecklat chiral effektiv fältteori (EFT) med pioner och nukleoner som frihetsgrader\n",
    "\n",
    "![](figures/chiral_force_472x413.png) "
   ]
  },
  {
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   },
   "source": [
    "### EFT parametrar\n",
    "För en EFT ryms okänd fysik inuti *\"lågenergikonstanter\"* (LECs), som alltså blir teoretiska parametrar.\n",
    "\n",
    "| Ordning\t    | Antal parametrar (LEC) |\n",
    "|---------------|-------------|\n",
    "| Leading Order (LO)   | 2 |\n",
    "| Next-to-Leading-Order (NLO) | 12 |\n",
    "| Next-to-Next-to-Leading-Order (N2LO) | 26 |\n",
    "| Next-to-Next-to-Next-to-Leading-Order (N3LO) | 41 |\n",
    "\n",
    "...fast det är värt att påpeka att letandet efter den *\"bästa\"* EFTn fortfarande pågår."
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "Givet en uppsättning parametrar är det möjligt att göra teoretiska prediktioner av (bland annat):\n",
    "* Gränserna för bunden kärnmateria (vilka isotoper kan existera i naturen).\n",
    "* Möjliga processer för kärnsyntesen (hur och var har våra grundämnen bildats).\n",
    "* Atomkärnors respons till olika svaga processer \n",
    "  * detektion av mörk materia\n",
    "  * neutrinolöst dubbelt betasönderfall\n",
    "  * och andra effekter som skulle känneteckna fysik bortanför standradmodellen\n",
    "* Egenskaper hos bundna och instabila atomkärnor (spektroskopi) samt hos oändlig kärnmateria (neutronstjärnor, etc).\n",
    "* etc."
   ]
  },
  {
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   "source": [
    "Men i samtliga dessa fall krävs storskaliga beräkningar för att komma fram till själva prediktionen\n",
    "* Vi behöver t.ex. kunna lösa ett kvantmekaniskt mångkropparsproblem (atomkärna med $N$ nukleoner)<br/><br/>\n",
    "$H | \\Psi \\rangle = E | \\Psi \\rangle$\n",
    "<br/><br/>\n",
    "där både $H$ och $\\Psi$ beror på $N$ stycken koordinater och $N$ uppsättningar med intriniska frihetsgrader (spinn, isospinn).\n",
    "\n",
    "* Detta problem kan formuleras på olika sätt:\n",
    "  * t.ex. som en $3(N-1)$-dimensionell integral, t.ex. 33 dimensioner för kol-12.\n",
    "  * Eller som ett matrisegenvärdesproblem<br/><br/>\n",
    "$\\Psi = \\sum_i^D c_i | \\phi_i\\rangle \\quad \\Rightarrow \\quad \\sum_j^D \\langle \\phi_j | H | \\phi_i \\rangle = E c_i$ <br/><br/>\n",
    "med problemet att $D$ kan vara $10^{10}$ eller ännu större!\n",
    "\n",
    "... och dessutom är prediktionen väldigt lite värd utan en uppskattning av dess precision"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "# Den vetenskapliga metoden"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "> Att vara osäker är obehagligt..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "> ... fast att vara helt säker är å andra sidan helt absurt!\n",
    "\n",
    "\n",
    "Voltaire (fritt översatt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![](figures/scientific_wheel.png)\n",
    "[Källkod till figuren med XKCD font finns i extramaterialet](SNF_presentation_extra.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "# Att kvantifiera osäkerhet: Statistik\n",
    "## Två olika synsätt: Frekventist eller Bayesian?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "| Statistiker\t    | Definition av sannolikhet |\n",
    "|---------------|-------------|\n",
    "| Frekventist   | $P(A)$ = relativ frekvens med vilken $A$ uppkommer för identiska repetitioner av ett experiment. <br/><br/>$A$ är en proposition angående slumpmässiga variabler. |\n",
    "| Bayesian   | $P(A \\vert B)$ = ett reellt tal som mäter plausibiliteten för hypotes $A$ givet den information/data som representeras av $B$. <br/><br/>$A$ kan vara vilken sorts hypotes som helst; måste inte begränsas till propositioner angående slumpmässiga variabler. |\n",
    "\n",
    "För Bayesianer inbegriper konceptet ```\"sannolikhet\"``` uttalanden om hur säker man är på något (```\"degrees of certainty\"```). \n",
    "\n",
    "Ett uttalande om sannolikhet är fundamentalt kopplat till den kunskap som personen besitter, som i sin tur är baserad på tillgänglig data och annan information ```\"prior information\"```. Notera att olika personer kan vara olika säkra på ett påstående beroende på vilken information de besitter.  "
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "Betrakta en modell med ett antal fria parametrar $p$. Bayesianer utgår från [Bayes teorem](http://en.wikipedia.org/wiki/Bayes\\'_theorem), som är en fundamental sannolikhetslag:\n",
    "\n",
    "$$ P(p~|~D,I) = \\frac{P(D~|~p,I)~P(p~|~I)}{P(D~|~I)} $$\n",
    "\n",
    "Låt oss studera de olika faktorerna i detta uttryck:\n",
    "\n",
    "- $P(p~|~D,I)$: Aposteriorifördelning (**posterior**), sannolikheten för modellparametrarna givet data $D$ och information $I$. Detta är generellt den kunskap som vi vill kunna kvantifiera.\n",
    "- $P(D~|~p,I)$: Likelihood-funktion (**likelihood**), vilken dyker upp även i frekventistmetoden där man ofta söker att maximera den.\n",
    "- $P(p~|~I)$: Apriorifördelning (**prior**), vilken beskriver vad vi vet om modellen före insamlingen an data $D$.\n",
    "- $P(D~|~I)$: Datasannolikhet (**Data probability**), vilket i praktiken motsvarar en normaliseringskonstant.\n",
    "\n",
    "Notera att denna formulering är *fundamentalt annorlunda* jämfört med frekventisters filosofi. Den senare påstår nämligen att begreppet sannolikhet inte har någon mening för modellparametrar. Istället pratar man om sannolikhet (eller frekvens) att observera viss data given en fix modell."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Dessa två angreppssätt för att göra statistisk inferens är ofta ekvivalenta, åtminstone för enkla problem. Men det Bayesianska, med sina explicita uttalanden om <b>förhandsinformation</b>, och sin tydliga koppling till <b>tillgänglig data</b> är mer naturlig inom naturvetenskap.\n",
    "\n",
    "Två situationer där skillnaderna är speciellt tydliga gäller:\n",
    "1. Hanterandet av \"irritationsparametrar\" (<b>nuisance parameters</b>).\n",
    "2. Den subtila (men otroligt viktiga) skillnaden mellan frekventisters <b>konfidensintervall</b> och bayesianska <b>kredibilitetsintervall</b>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exempel #1: Ett Bayesianskt biljardspel\n",
    "På engelska. \n",
    "Hämtat från bloggposten [Frequentism and Bayesianism II: When Results Differ](http://jakevdp.github.io/blog/2014/06/06/frequentism-and-bayesianism-2-when-results-differ/) \n",
    "\n",
    "This example of nuisance parameters dates all the way back to the posthumous [1763 paper](http://www.stat.ucla.edu/history/essay.pdf) written by Thomas Bayes himself. The particular version of this problem used here is borrowed from [Eddy 2004](ftp://selab.janelia.org/pub/publications/Eddy-ATG3/Eddy-ATG3-reprint.pdf).\n",
    "\n",
    "The setting is a rather contrived game in which Alice and Bob bet on the outcome of a process they can't directly observe:\n",
    "\n",
    "Alice and Bob enter a room. Behind a curtain there is a billiard table, which they cannot see, but their friend Carol can. Carol rolls a ball down the table, and marks where it lands. Once this mark is in place, Carol begins rolling new balls down the table. If the ball lands to the left of the mark, Alice gets a point; if it lands to the right of the mark, Bob gets a point.  We can assume for the sake of example that Carol's rolls are unbiased: that is, the balls have an equal chance of ending up anywhere on the table.  The first person to reach **six points** wins the game.\n",
    "\n",
    "Here the location of the mark (determined by the first roll) can be considered a nuisance parameter: it is unknown, and not of immediate interest, but it clearly must be accounted for when predicting the outcome of subsequent rolls. If the first roll settles far to the right, then subsequent rolls will favor Alice. If it settles far to the left, Bob will be favored instead."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Given this setup, here is the question we ask of ourselves:\n",
    "\n",
    "> In a particular game, after eight rolls, Alice has five points and Bob has three points. What is the probability that Bob will go on to win the game?\n",
    "\n",
    "Intuitively, you probably realize that because Alice received five of the eight points, the marker placement likely favors her. And given this, it's more likely that the next roll will go her way as well. And she has three opportunities to get a favorable roll before Bob can win; she seems to have clinched it.  But, **quantitatively**, what is the probability that Bob will squeak-out a win?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### A Naive Frequentist Approach\n",
    "Someone following a classical frequentist approach might reason as follows:\n",
    "\n",
    "To determine the result, we need an intermediate estimate of where the marker sits. We'll quantify this marker placement as a probability $p$ that any given roll lands in Alice's favor.  Because five balls out of eight fell on Alice's side of the marker, we can quickly show that the maximum likelihood estimate of $p$ is given by:\n",
    "\n",
    "$$\n",
    "\\hat{p} = 5/8\n",
    "$$\n",
    "\n",
    "(This result follows in a straightforward manner from the [binomial likelihood](http://en.wikipedia.org/wiki/Binomial_distribution)). Assuming this maximum likelihood probability, we can compute the probability that Bob will win, which is given by:\n",
    "\n",
    "$$\n",
    "P(B) = (1 - \\hat{p})^3\n",
    "$$\n",
    "\n",
    "That is, he needs to win three rolls in a row. Thus, we find that the following estimate of the probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Naive Frequentist Probability of Bob Winning: 0.05\n"
     ]
    }
   ],
   "source": [
    "p_hat = 5. / 8.\n",
    "freq_prob = (1 - p_hat) ** 3\n",
    "print(\"Naive Frequentist Probability of Bob Winning: %.2f\" %freq_prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In other words, we'd give Bob the following odds of winning:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Odds against Bob winning: 17 to 1\n"
     ]
    }
   ],
   "source": [
    "print(\"Odds against Bob winning: %i to 1\" %((1. - freq_prob) / freq_prob))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we've estimated using frequentist ideas that Alice will win about 17 times for each time Bob wins. Let's try a Bayesian approach next."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Bayesian approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also approach this problem from a Bayesian standpoint. This is slightly more involved, and requires us to first define some notation.\n",
    "\n",
    "We'll consider the following random variables:\n",
    "\n",
    "- $B$ = Bob Wins\n",
    "- $D$ = observed data, i.e. $D = (n_A, n_B) = (5, 3)$\n",
    "- $p$ = unknown probability that a ball lands on Alice's side during the current game\n",
    "\n",
    "We want to compute $P(B~|~D)$; that is, the probability that Bob wins given our observation that Alice currently has five points to Bob's three."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The general Bayesian method of treating nuisance parameters is *marginalization*, or integrating the joint probability over the entire range of the nuisance parameter. In this case, that means that we will first calculate the joint distribution\n",
    "\n",
    "$$\n",
    "P(B,p~|~D)\n",
    "$$\n",
    "\n",
    "and then marginalize over $p$ using the following identity:\n",
    "\n",
    "$$\n",
    "P(B~|~D) \\equiv \\int_{-\\infty}^\\infty P(B,p~|~D) {\\mathrm d}p\n",
    "$$\n",
    "\n",
    "This identity follows from the definition of conditional probability, and the law of total probability: that is, it is a fundamental consequence of probability axioms and will always be true. Even a frequentist would recognize this; they would simply disagree with our interpretation of $P(p)$ as being a measure of uncertainty of our own knowledge."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Building our Bayesian Expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute this result, we will manipulate the above expression for $P(B~|~D)$ until we can express it in terms of other quantities that we can compute."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll start by applying the following definition of [conditional probability](http://en.wikipedia.org/wiki/Conditional_probability#Definition) to expand the term $P(B,p~|~D)$:\n",
    "\n",
    "$$\n",
    "P(B~|~D) = \\int P(B~|~p, D) P(p~|~D) dp\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we use [Bayes' rule](http://en.wikipedia.org/wiki/Bayes%27_theorem) to rewrite $P(p~|~D)$:\n",
    "\n",
    "$$\n",
    "P(B~|~D) = \\int P(B~|~p, D) \\frac{P(D~|~p)P(p)}{P(D)} dp\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Finally, using the same probability identity we started with, we can expand $P(D)$ in the denominator to find:\n",
    "\n",
    "$$\n",
    "P(B~|~D) = \\frac{\\int P(B~|~p,D) P(D~|~p) P(p) dp}{\\int P(D~|~p)P(p) dp}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the desired probability is expressed in terms of three quantities that we can compute. Let's look at each of these in turn:\n",
    "\n",
    "- $P(B~|~p,D)$: This term is exactly the frequentist likelihood we used above. In words: given a marker placement $p$ and the fact that Alice has won 5 times and Bob 3 times, what is the probability that Bob will go on to six wins?  Bob needs three wins in a row, i.e. $P(B~|~p,D) = (1 - p) ^ 3$.\n",
    "- $P(D~|~p)$: this is another easy-to-compute term. In words: given a probability $p$, what is the likelihood of exactly 5 positive outcomes out of eight trials? The answer comes from the well-known [Binomial distribution](http://en.wikipedia.org/wiki/Binomial_distribution): in this case $P(D~|~p) \\propto p^5 (1-p)^3$\n",
    "- $P(p)$: this is our prior on the probability $p$. By the problem definition, we can assume that $p$ is evenly drawn between 0 and 1.  That is, $P(p)$ is a uniform probability distribution in the range from 0 to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Putting this all together, canceling some terms, and simplifying a bit, we find\n",
    "$$\n",
    "P(B~|~D) = \\frac{\\int_0^1 (1 - p)^6 p^5 dp}{\\int_0^1 (1 - p)^3 p^5 dp}\n",
    "$$\n",
    "where both integrals are evaluated from 0 to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These integrals might look a bit difficult, until we notice that they are special cases of the [Beta Function](http://en.wikipedia.org/wiki/Beta_function):\n",
    "$$\n",
    "\\beta(n, m) = \\int_0^1 (1 - p)^{n - 1} p^{m - 1}\n",
    "$$\n",
    "The Beta function can be further expressed in terms of gamma functions (i.e. factorials), but for simplicity we'll compute them directly using Scipy's beta function implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(B|D) = 0.09\n"
     ]
    }
   ],
   "source": [
    "from scipy.special import beta\n",
    "bayes_prob = beta(6 + 1, 5 + 1) / beta(3 + 1, 5 + 1)\n",
    "\n",
    "print(\"P(B|D) = %.2f\" %bayes_prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The associated odds are the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bayesian odds against Bob winning: 10 to 1\n"
     ]
    }
   ],
   "source": [
    "print(\"Bayesian odds against Bob winning: %i to 1\" %((1. - bayes_prob) / bayes_prob))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we see that the Bayesian result gives us 10 to 1 odds, which is quite different than the 17 to 1 odds found using the frequentist approach. So which one is correct?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Brute-force (Monte Carlo) approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this type of well-defined and simple setup, it is actually relatively easy to use a Monte Carlo simulation to determine the correct answer. This is essentially a brute-force tabulation of possible outcomes: we generate a large number of random games, and simply count the fraction of relevant games that Bob goes on to win. The current problem is especially simple because so many of the random variables involved are uniformly distributed.  We can use the ``numpy`` package to do this as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(Sanity check passed)\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "\n",
    "# play 100000 games with randomly-drawn p, between 0 and 1\n",
    "p = np.random.random(100000)\n",
    "\n",
    "# each game needs at most 11 rolls for one player to reach 6 wins\n",
    "rolls = np.random.random((11, len(p)))\n",
    "\n",
    "# count the cumulative wins for Alice and Bob at each roll\n",
    "Alice_count = np.cumsum(rolls < p, 0)\n",
    "Bob_count = np.cumsum(rolls >= p, 0)\n",
    "\n",
    "# sanity check: total number of wins should equal number of rolls\n",
    "total_wins = Alice_count + Bob_count\n",
    "assert np.all(total_wins.T == np.arange(1, 12))\n",
    "print(\"(Sanity check passed)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of suitable games: 11068\n",
      "Number of these games Bob won: 979\n",
      "Monte Carlo Probability of Bob winning: 0.09\n",
      "MC Odds against Bob winning: 10 to 1\n"
     ]
    }
   ],
   "source": [
    "# determine number of games which meet our criterion of (A wins, B wins)=(5, 3)\n",
    "# this means Bob's win count at eight rolls must equal 3\n",
    "good_games = Bob_count[7] == 3\n",
    "print(\"Number of suitable games: {0}\".format(good_games.sum()))\n",
    "\n",
    "# truncate our results to consider only these games\n",
    "Alice_count = Alice_count[:, good_games]\n",
    "Bob_count = Bob_count[:, good_games]\n",
    "\n",
    "# determine which of these games Bob won.\n",
    "# to win, he must reach six wins after 11 rolls.\n",
    "bob_won = np.sum(Bob_count[10] == 6)\n",
    "print(\"Number of these games Bob won: {0}\".format(bob_won.sum()))\n",
    "\n",
    "# compute the probability\n",
    "mc_prob = bob_won.sum() * 1. / good_games.sum()\n",
    "print(\"Monte Carlo Probability of Bob winning: {0:.2f}\".format(mc_prob))\n",
    "print(\"MC Odds against Bob winning: {0:.0f} to 1\".format((1. - mc_prob) / mc_prob))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Monte Carlo approach gives 10-to-1 odds on Bob, which agrees with the Bayesian approach. Apparently, our naive frequentist approach above was flawed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Discussion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "This example shows several different approaches to dealing with the presence of a nuisance parameter *p*. The Monte Carlo simulation gives us a close brute-force estimate of the true probability (assuming the validity of our assumptions), which the Bayesian approach matches. The naïve frequentist approach, by utilizing a single maximum likelihood estimate of the nuisance parameter $p$, arrives at the wrong result.\n",
    "\n",
    "We should emphasize that **this does not imply frequentism itself is incorrect**. The incorrect result above is more a matter of the approach being \"naive\" than it being \"frequentist\". There certainly exist frequentist methods for handling this sort of nuisance parameter – for example, it is theoretically possible to apply a transformation and conditioning of the data to isolate the dependence on $p$ – but it's hard to find any approach to this particular problem that does not somehow take advantage of Bayesian-like marginalization over $p$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Another potential point of contention is that the question itself is posed in a way that is perhaps unfair to the classical, frequentist approach. A frequentist might instead hope to give the answer in terms of null tests or confidence intervals: that is, they might devise a procedure to construct limits which would provably bound the correct answer in $100\\times(1 - p)$ percent of similar trials, for some value of $p$ – say, 0.05 (note this is a different $p$ than the $p$ we've been talking about above). This might be classically accurate, but it doesn't quite answer the question at hand. I'll leave discussion of the meaning of such confidence intervals for my follow-up post on the subject.\n",
    "\n",
    "There is one clear common point of these two potential frequentist responses: both require some degree of effort and/or special expertise; perhaps a suitable frequentist approach would be immediately obvious to someone with a PhD in statistics, but is most definitely *not* obvious to a statistical lay-person simply trying to answer the question at hand. In this sense, I think Bayesianism provides a better approach for this sort of problem: by simple algebraic manipulation of a few well-known axioms of probability within a Bayesian framework, we can straightforwardly arrive at the correct answer without need for other special expertise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exempel #2: Linjär kurvanpassning med dataavikelser (outliers)\n",
    "På engelska.\n",
    "Hämtat från bloggposten [Frequentism and Bayesianism II: When Results Differ](http://jakevdp.github.io/blog/2014/06/06/frequentism-and-bayesianism-2-when-results-differ/) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "One situation where the concept of nuisance parameters can be helpful is accounting for outliers in data. Consider the following dataset, relating the observed variables $x$ and $y$, and the error of $y$ stored in $e$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "x = np.array([ 0,  3,  9, 14, 15, 19, 20, 21, 30, 35,\n",
    "              40, 41, 42, 43, 54, 56, 67, 69, 72, 88])\n",
    "y = np.array([33, 68, 34, 34, 37, 71, 37, 44, 48, 49,\n",
    "              53, 49, 50, 48, 56, 60, 61, 63, 44, 71])\n",
    "e = np.array([ 3.6, 3.9, 2.6, 3.4, 3.8, 3.8, 2.2, 2.1, 2.3, 3.8,\n",
    "               2.2, 2.8, 3.9, 3.1, 3.4, 2.6, 3.4, 3.7, 2.0, 3.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We'll visualize this data below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x136659b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(x, y, e, fmt='.k', ecolor='gray');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Our task is to find a line of best-fit to the data. It's clear upon visual inspection that there are some outliers among these points, but let's start with a simple non-robust maximum likelihood approach. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Like we saw in the previous post, the following simple maximum likelihood result can be considered to be either frequentist or Bayesian (with uniform priors): in this sort of simple problem, the approaches are essentially equivalent.\n",
    "\n",
    "We'll propose a simple linear model, which has a slope and an intercept encoded in a parameter vector $\\theta$. The model is defined as follows:\n",
    "$$\n",
    "\\hat{y}(x~|~\\theta) = \\theta_0 + \\theta_1 x\n",
    "$$\n",
    "Given this model, we can compute a Gaussian likelihood for each point:\n",
    "$$\n",
    "p(x_i,y_i,e_i~|~\\theta) \\propto \\exp\\left[-\\frac{1}{2e_i^2}\\left(y_i - \\hat{y}(x_i~|~\\theta)\\right)^2\\right]\n",
    "$$\n",
    "The total likelihood is the product of all the individual likelihoods. Computing this and taking the log, we have:\n",
    "$$\n",
    "\\log \\mathcal{L}(D~|~\\theta) = \\mathrm{const} - \\sum_i \\frac{1}{2e_i^2}\\left(y_i - \\hat{y}(x_i~|~\\theta)\\right)^2\n",
    "$$\n",
    "This should all look pretty familiar if you read through the previous post. This final expression is the log-likelihood of the data given the model, which can be maximized to find the $\\theta$ corresponding to the maximum-likelihood model. Equivalently, we can minimize the summation term, which is known as the *loss*:\n",
    "$$\n",
    "\\mathrm{loss} = \\sum_i \\frac{1}{2e_i^2}\\left(y_i - \\hat{y}(x_i~|~\\theta)\\right)^2\n",
    "$$\n",
    "This loss expression is known as a *squared loss*; here we've simply shown that the squared loss can be derived from the Gaussian log likelihood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Standard Likelihood Approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Following the logic of the previous post, we can maximize the likelihood (or, equivalently, minimize the loss) to find $\\theta$ within a frequentist paradigm. For a flat prior in $\\theta$, the maximum of the Bayesian posterior will yield the same result. (note that there are good arguments based on the principle of maximum entropy that a flat prior is not the best choice here; we'll ignore that detail for now, as it's a very small effect for this problem).\n",
    "\n",
    "For simplicity, we'll use scipy's ``optimize`` package to minimize the loss (in the case of squared loss, this computation can be done more efficiently using matrix methods, but we'll use numerical minimization for simplicity here)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6XGoQGBiI5OTkKne3vOLj44Pp06dj3bp1WLFiBaysrODv7w9ra2ukpqaioKCALeSvCoRUKsWRI0ewYMECKBSKBscoEAiwevVqfPPNN5BKpejYsSM+//xz9tbAxrZ3794q/Z1t27bFqVOnalzP1NQUy5cvx9SpU3Hw4EGMGzcO+/btw+rVqzFjxgyUlpaiZ8+e2LJlS63XGFS1du1arFu3DsuXL0deXh66dOmCkJAQ9iKctbU1fvnlF6xevRoTJ06EQCBA//79sX//fvaaxavusx07dmDVqlVwcXHBlClT8Pvvv9c7Ll9fX4SFhUEsFuO7776Dv78/hg4dis8//xyzZs164zqjRo3C3r17sX37dnzxxRfIz8+HmZkZBgwYwN5NAgD29vbYuXMn/v3vf0MsFqNz584YN24c58LpRx99hDt37mDhwoUQCATw8/NDcHAwewwnTZqEW7du4Z///CeKi4vRqVMnjB8/HnFxcZzbQl9nZmZW6zH18PDA+vXrsWnTJmzbtg09e/bEjBkzsHr16lp/bp999lmVZVOnTsW8efNqPdbe3t5Yvnw5du/ejTVr1kAoFMLDwwMLFy5kcy4sLMTGjRtx//59mJubw8fHB/Pmzas1rpZEQDMWEcJvp0+fxuTJkxEdHY1u3bqpOxzShKjLhRBCeIIKOiGE8AR1uRBCCE/QGTohhPCEWu9yefjweb3WEwgEaNPGBI8fF2jc4Dn1RTlTznykbfkCDc+5XbvqR2jVyDN0HZ2XP5Rm+KJji0E5awdty1nb8gWaNmct+jESQgi/UUEnhBCeoIJOCCE8QQWdEEJ4ggo6IYTwBBV0QgjhCSrohBDCE1TQCSGEJ2g89BYqPz8P+/a9nLF84sRgWFq2rmUNQoi2o4JOCOGt10+MzM0t1BxR06IuF0II4Qkq6IQQwhNU0AkhhCeooBNCCE9QQSeEEJ6ggk4IITxBBZ0QQniCCjohhPAEFXRCCOEJKuiEEMITVNAJIYQneDmWi7aN30AIIQCdoRNCCG/w8gydD8rKyhAXF4e7d+/i3r1cLF/+tbpDIkTjvP45WrJkJfT19dUdVpOhgt5CrV+/BidPngQAbNu2GUZGRvjhh+/VHBUhmuX1z5FQaITFi5eqOaqmU2uXi0KhgLOzM+efvb09QkJCkJ+fj5kzZ8LV1RWenp4IDQ1tjpi1QkrKJc7z8+fPqSkSQjTX65+jCxf4/TmqtaCLRCJcvHiR/bd582a0bdsWM2fOREhICIyNjZGUlIQNGzbg+++/x7Vr15ojbt5zcurHee7q2l9NkRCiuV7/HLm48PtzVKcul4KCAnz11VdYtmwZzMzMEBcXh5iYGBgaGqJv374IDAxEaGgoQkJCmiperTFnzpdIT09FdnY2fHz8sXDhYnWHRIjGef1ztGDBInWH1KTqVNB//vln9OzZEyNHjsSVK1egp6cHGxsbtt3W1haxsbEqb08gEECnHvfZ6OgIOP+/TldXwHlc+bmmEAoNMHLkSADA5MlTYGhoAKD6nPmotuPMR9qWc1Pn+/rnSCg0aJL91EVT5qxyQS8oKMAvv/yC//znPwCAwsJCCIVCzmuEQiGKi4tV3nmbNiYQCOqflIWFSTUtpewjc3NjWFqa1nsf6sPN4VWu1efMX5Qz/zVdvi23FjRFzioX9Li4OHTs2BH9+r3skzIyMqpSvIuLi2FsbKzyzh8/Lqj3GbqFhQny8gqgVDJV2vPzC197rP7fynX1eg46OoY15sxHtR1nPtK2nJs635ZYCxqac02/lFQu6AkJCfDz82Ofd+7cGeXl5cjJyUHHjh0BAJmZmejevbvKgTEMg4oKlV9ehVLJoKKi6g+k8rKKije/pqV7PYdXB766nPmMcua/psq3JdeCpshZ5fPjlJQU9uwcAExNTeHt7Y01a9agqKgIqampiIyMxJgxYxo1QEIIIapRqaBXVFTg/v37aNeuHWf5ypUrUV5eDg8PD8yePRvz58+Hk5NTkwRKCCGkZip1uejq6uLq1atVlltYWGD9+vWNHhQhhJC6o8G5CCGEJ3g5lou2DchDCCEATwu6tg3IQwghAE+7XLRtQB5CCAF4WtC1bUAeQggBeNrlom0D8hBC3szc3AIzZsxVdxjNhpcFXV9fnx2QZ+LEYI28IKptb0RCSMPxssuFEEK0ES/P0AkhNcvPz8O+fTsAvPwr1tzcQs0RkcZAZ+iEEMITVNAJIYQnqKATQghPUEEnhBCeoIJOCCE8QQWdEEJ4ggo6IYTwBBV0QgjhCSrohBDCE/RNUUJ4jL4Rql3oDJ0QQniCl2foNFIhIUQb0Rk6IYTwBBV0QghpBhkZN7F27XcYNswdNjY2yMj4s9H3wcsuF0JIzcrKyhAXF4e7d+/i3r1cLFmyUiMngmnpMjP/gkIRDrk8HGlpqexygUCAJ08eo0uXbo26PyrohGih9evX4OTJkwCAbds2Qyg0wuLFS9UcFT/cvn0Lcnk4FIpwpKRc5LS1a9ceIpEEU6cGo0cPB1RUMI26byrohGihlJRLnOcXLpxTUyT8kJ19FwqFDHL5IVy4cJ7T1qZNGwQEiCGRSDFo0BAYGOjB0tIUT568aPQ4qKAT0gRa+v3fTk79kJycxD53cemvxmg00/379xARIYNMFoazZ09z2lq3bo2AABFEoiAMHTocenrNU2qpoBOihebM+RLp6anIzs6Gj48/FixYpO6QNEJubi4iImRQKMKRnJwEhvm7y6RVK3P4+wdCIpFi2DBPtVyToIJOiBbS19fHyJEjAbz8C4IuiFbv0aNHiIpSQC4PQ1LSSSiVSrbN1NQMfn4BEIuD4OExAoaGhmqMlAo6IYRU8eTJY0RHR0IuD8PJkydQUVHBthkbm8DX1w9i8Vh4eXlDKBSqMVIuKuiEEAIgL+8pjhyJhkx2CCdOHEd5eTnbZmRkhFGjfCEWS+HtPQrGxsZqjLR6VNAJ4TG637xmz58/w+HDUVAowpGQEI+ysjK2TSgUwtt7NMTiIIwa5QsTExM1RqoaKuiE8Bjdb17VixcvEBt7GDJZGBIS4lBSUsK2GRgYYMSIkRCLpfDx8YOpqZkaI607KuiE8Bjdb/5SQUEB4uNjIZOFIS4uBsXFxWybvr4+PD1HQCyWwtfXH61amasx0oZRqaDfv38fS5cuxdmzZ2FqaopPPvkEkydPRn5+PhYtWoTk5GSYmZlh5syZePfdd5s6ZkKIirT5fvOioiLExx+FXB6Go0ePoLCwkG3T09PDsGEekEjGws8vABYWrdUYaeOptaAzDIMZM2Zg4MCB2LRpE7KysjBx4kT06dMHu3btgrGxMZKSknD9+nVMnToVjo6OsLe3b47YCSG10Lb7zYuLi5GQEA+5PAwxMYdRUPD3tzF1dHQwdKgHJBIp/P0DYWnZRo2RNo1aC3pKSgpyc3Mxb9486OrqokePHjhw4AAMDQ0RFxeHmJgYGBoaom/fvggMDERoaChCQkKaI3ZCWqyWcjFSG+43Ly0tRWLiMchkYThyJBrPnz9j2wQCAQYPHgqxWIqAABHatWunxkibXq0FPT09HT169MDq1asREREBU1NTTJ8+HXZ2dtDT04ONjQ37WltbW8TGxqq8c4FAAJ16DOCroyPg/K8NKGfNsmHDWs7FSCMjI4SELKt1vcbOWVdXwHn86nl1y5tbffMtKyvDiRPHIZOFISoqEvn5eWybQCCAu/sgiMVSiEQSdOjQoVFjbqimfF/XWtDz8/Nx+vRpuLu7IyEhAWlpafjkk0/w008/VbmhXigUci421KZNGxMIBPVPysKi5d9G1NgoZ82QlpbCeZ6aehGWlqYqr994OZeyj8zNjSvFUN1y9VAl3/LyciQkJODgwYMICwvDkydPOO2DBg3C+PHj8c4778Da2rqpQm00TfG+rrWgGxgYwNzcHNOmTQMAuLi4wMfHBxs2bKhSvIuLi+t0w/3jxwX1PkO3sDBBXl4BlMrGHX6ypaKcNSvnPn2c2DN0AOjb11ml0fUaO+f8/MLXHhvUuLy51ZZvRUUFkpJOQSY7hIgIOR4/fsxpd3HpD4kkCGJxEDp1+ru3oClGMmwsDT3GNf3yrbWg29raoqioCOXl5eyIYRUVFejduzfOnTuHnJwcdOzYEQCQmZmJ7t27qxwYwzCo9I3aOlMqmUYfT7ilo5xblupGVZw9ey7S0lLYi5Hz5y+qUw6NlXPlbVRU/L3N6parS+V8lUolzpxJZov4w4e5nNc6OTlDJAqCSCRB585d2OXqzqGumuJ9XWtBHzJkCFq1aoU1a9bgyy+/RGpqKo4ePYqdO3ciOzsba9aswddff42bN28iMjISP/30U6MGSIgmaukXI1vaROovi/gZKBRhUChkuH//HqfdwcERYnEQRKIgdO3auLP88EmtBV0oFGLv3r1YsWIFBg8eDFNTU/zzn/9Ev379sHLlSixduhQeHh4wNjbG/Pnz4eTk1BxxE0I0HMMwOH/+PI4cicBvvx1EdvZdTru9fS+IxVKIxVJ0795DTVFqFpW+WNS5c2ds3769ynILCwusX7++0YMihPATwzBITb3ETtF2+/YtTnv37j3YIm5v30tNUWou+uo/IaRJMQyDtLTL/5ssOQxZWZmc9u7du0MkCsKYMUHo3duhQXe+aTsq6ISQJnH16hXI5Ycgl4cjI+NPTtvbb3eBWByEoCApPD2H4OnTAo27qNkSUUEnhDSamzdvQCY7BIUiHNevX+O0depkA5EoCBKJFE5OzhAIXn6hic7IGw8VdEJIg/z115+Qy8Mhl4fjypU0TpuVVUeIRC/vE3d1HUDFu4lRQSeEx5rq9sSsrMz/9YmH4/Jl7rdi27fvAJFIApFICje3gdCpz7cHSb1QQSekCbS0+7wbw507t6FQyCCXH8KlSxc5bW3btkVgoBhisRTu7oOhq6urpii1GxV0Qki1srPvIiJCBrk8HOfPn+W0WVpaIiBADLE4CIMHD2W/SU7Uh44AIYTj/v17bBE/cyaZ02ZhYQF//zEQi6UYOnR4i/sGrLajgk4IQW5uLiIj5ZDLw5CcnASG+fsWwlatzOHnFwCxOAjDh3vBwEA9A3mR2lFBJ6QBWspEFvXx+PFjREUpIJeH4dSp/0KpVLJtJiam8PX1h0QyFp6eI2BoaKjGSImqqKAT0gDr16/hTGQhFBph8eKlao6qek+fPkF0dCTk8jD897+JqKg03KmxsQl8fHwhFo+Fl5c3jIyM1BgpqQ8q6IQ0QErKJc7zCxfOqSmS6uXn5+Hw4SjI5WFITExAeXk522ZkZISRI30gkUjh7T26TvMZkJaHCjohDeDk1A/JyUnscxeX/mqM5m/Pnz/DkSPRUCjCkZAQj9LSv2coMjQ0hLf3aIjFQRg1yhempuqdrYg0HirohDTAnDlfIj09lZ3IYsGCRWqL5cWLFzh69AhksjAcO3YUJSUlbJu+vj68vLwhFkvh6+sPM7NWaouTNB0q6KRFqjwT0OTJU2Bqaq7miN5M3RNZFBYWIi4uBnJ5OOLiYlBUVMS26enpwdNzBESiIPj5BbCzKRH+ooJOiIYpLi5GfPxRKBRhiIk5gsLCArZNV1cXw4Z5QCIZCz+/ALRubanGSElzo4JOiAYoKSnB8ePHIJMdQkzMYbx48Zxt09HRwZAhwyEWByEgQIQ2bdqoMVKiTlTQCWmhSktLceJEAuTycBw+HIVnz/LZNoFAgMGDh0IkCkJgoBjt2rVTY6SkpaCCTkgLUlZWhpiYGOzduw9RURHIy8vjtA8cOAgSiRSBgWJ06PCWmqIkLRUVdELUrLy8HElJJyGXhyEqSoEnT55w2l1dB0AikWLMGAk6drRWU5REE1BBJxql8t0vEycGa+ydGxUVFUhOToJcHobISAUePXrIaXd2doVIFASRSAIbm7fVFCXRNFTQCWkmSqUSZ86chlx+CBERcuTmPuC0Ozo6IShIig8//AAWFu1pjk1SZ1TQSYtUedCr+/cfIiRkhcYMelUZwzA4f/4s5PIwKBQy3LuXw2nv3bsPxOKXU7R17doduroCWFqa4smTF2qKmGgyKuikRao86NXWrT/C0FDYoge9qoxhGFy6dAEyWRgiImS4e/cOp93Ozh5isRRisRQ9evRUU5SEj6iofzwYAAAaiUlEQVSgkxZJEwa9qoxhGKSnX0Z8fBzk8nDcvp3Fae/WrTtbxHv16q2eIAnvUUEnTaKhFy9b6qBXlTEMg2vXriI+Ph7p6elV7k7p0sUWEslYiERBcHDoQzPekyZHBZ20SJUHvfL1Ve+gV6+7du3q//rEw3Hz5g1O29tvd8aYMRJIJFL07duPijhpVlTQSYtUedCryZOnqP2C6J9/3oRcHga5PAzXrl3ltHXsaA2RKAgSiRTOzq5UxInaUEEnpBp//ZWBiAgZZLIwpKdf5rS99ZYVxowRQywei/79B0BHR0dNURLyNyropMV7/vwZ9uzZDgAQid5p0n3dupUFhUIGuTwMqancC7Pt23f4XxGXws3NnYo4aXGooBOtd/fuHSgUMigUYbhw4TynrW3btggIEEMikcLdfTB0dXXVFCUhtaOCTrTSvXs5UCjCIZeH49y5M5y21q1bIzBQDJEoCEOGDIOeHn1MiGagdyrRWM+fP6vTrZEPHjxAZOTLPvHTp//gtJmbW8DPLwASiRTDhnmq/SIsIfVBBZ3w2sOHDxEVpYBcHoakpJNgmL/HRzEzawVfX39IJFJ4eIyAgYGBGiMlpOFUKug///wz1q1bxzlr+c9//oMePXpg0aJFSE5OhpmZGWbOnIl33323yYIl2sPc3AKzZn0JS0tTZGberdO6T548RnR0JGSyMJw8mQilUsm2mZiYwsfHDxLJWHh6joBQKGzs0AlRG5UK+tWrV/HFF19gypQpnOWzZ8+GsbExkpKScP36dUydOhWOjo6wt7dvkmAJqTxo161bd9CpU0fo6uoiPz8P0dGRkMvDcOLEcZSXl7PrGBsbY/RoX4hEUnh7j4KRkZEaMyCk6ahc0MeOHctZVlBQgLi4OMTExMDQ0BB9+/ZFYGAgQkNDERISotLOBQIB6nPnl46OgPO/NlBHzvn5eeztgpMnT6nT1/d1dQWcx5Wfq+pVrpW/qLNt24/soF07d25Hz549wTAMvvnmG5SVlbGvEwqFGDXKB0FBYzFy5GiYmJjUef/qoG3vbW3LF2janGst6EVFRcjKysKePXswf/58tGrVClOmTEHv3r2hp6cHGxsb9rW2traIjY1Veedt2pg06Ft1Fhaa8SFtTM2bcyn7yNzcGJaWps20LlerVn+fUV++nMJpu3Hj76/eGxoaws/PD+PGjcOYMWNgalr/faqbtr23tS1foGlyrrWgP3r0CC4uLnjvvfewYcMGpKamYvr06fj444+r9D8KhUIUFxervPPHjwvqfYZuYWGCvLwCKJXaMQmAOnLOzy987bHqFw0bsu4rr3K+f/8x0tLSkJaWxingr/Ts2RPTps2AVPouWrVqBQAoLYVGjimube9tbcsXaHjONZ0c1VrQbWxs8Msvv7DP+/fvD7FYjHPnzlUp3sXFxTA2NlY5MIZhUFGh8surUCoZrZvVpTlzrryfioq67be4uJTt6753LxdLlqys062AhYWFSEiIQ3S0HAqFAiUlJZx2IyMjuLoOgLu7G0xNTSESSWFiYsab94O2vbe1LV+gaXKutaCnp6fj1KlT+PTTT9llJSUlsLKyQnl5OXJyctCxY0cAQGZmJrp3796oARLNVHmCim3bNkMoNKp1gori4mIcOxYHhSIMR44cRmFhwRtf5+7uDl9fX4hE70Ch+L3RYydEU9Va0I2NjbFp0ya8/fbbGD16NE6fPo2oqCj88ssveP78OdasWYOvv/4aN2/eRGRkJH766afmiJu0cKpOUFFSUoLExGOQy8Nx5Eg0nj9/xrbp6OjAw8MDWVm3kJn5F7v8wYMHb9oUIVqv1oJua2uLdevW4YcffsDChQvRoUMH/Otf/4KDgwNWrlyJpUuXwsPDA8bGxpg/fz6cnJyaI27SwtU0QUVZWRlOnEiAXB6O6OhIPHuWz7YJBAK4uw+GWCyFSCRGr17d8Nlnn2Pr1h/Z11hbWzdPEoRoGJVuWxwxYgRGjBhRZbmFhQXWr1/f6EERzVd5ggofH3/MnbsAx48fg0IRjqgoBZ4+fcp5/YABAyGRSDFmjARvvWUF4O9bH7/44kukpaUgOzsbnp7e6NTJqtnzIUQT0Ff/SbUqf4mnrhc29fX1MWLECGRlZSEvLw8uLr3x+PFjzmtcXftDJJJCJJLA2rpTjdt6NdlF5X7zhsRHCB9RQSfVqs+FTaVSidOn/8DBg/shkx1CQQH3wqaTk/P/ulMkePvtzg2Kb+vWTXWOjxA+o4JOqqXqhU2lUolz585CLj8EhUKGBw/uc9p79XKAVPoORKIg2Np2bbT4Ll/mziJUXXyEaAsq6KRaNV3YZBgGFy6cg1wejogIGbKzuQNo2dnZo2NHKzg4OGDOnAV1GjZAVY6OjpyxzCvHR4g2ooJOqvX6hc358/8PKSkXIZO9nPH+zp3bnNf37Gn3v+6UILz11lvsWOVNZfr0z3Hz5nU2vgULFjXp/ghp6aigk2rp6+vD29sb9++/7EIZOnQAsrIyOa/p2rUbJBIpxOKxsLfvxY7Nk5+f1yzxvbpYOnFiMF0QJVqPCjqpgmEYXL16BQcP7sdvv+2rcndK585dIBZLIRZL0aePY4MGWCOENB4q6IR148Z1yGSHoFCE48aN65y2jh2tIZGMhUQihZOTMxVxQlogKuhaLiPjJtsnfvXqFU5bhw5vwda2C/r06YMFC0JgYdFaLTESQlRDBV0LZWb+BYUiHDJZGNLTubf+dejwFsaMEUMsHouePXti//5dAEBn5IRoACroGqbyLEKqzHT/yu3bt6BQyCCXhyEl5SKnrW3bdhgzRgyJZCzc3Nyhq6vL7qslMDe3wIwZc9nnrx63lPgIaSmooPNYdvZdKBQyKBRhOH+e+6WbNm3awN9fBIlEisGDh7JFnJBX8vPz2FtP63LyQNSHCjrP3L9/DxERMshkYTh79jSnzcLCAgEBIojFUgwdOhx6ejUf/tfPjAkhLRsVdB7Izc1FRIQMCkU4kpOTwDB/z4LSqpU5/PwCIJFIMWyYJwwM6j4VHCFEM1BB11AFBQXYv/8XxMYeQVLSSSiVSrbN1NQMvr7+EIul8PQcAUNDw2aPj87uCWl+VNA1yOPHj/Hbb/uxZ88eZGZmcs7EjY1N4OvrB5FIihEjRlaZwJuP6JcGIVxU0Fu4/Pw8HD4cBbk8DImJCSgvL2fbhEIhRo/2g1gshbf3qDpN0E0I4R8q6C3Q8+fPcORINOTyMCQkxKOsrIxtMzAwgJmZGXR0dDBmjAQrV66iMUxIk6AJRDQPFfQW4sWLF4iNPQy5PBzHjh1FSUkJ22ZgYIARI0Zi0qSJOHbsOLZv/w8AYMeO/8DMrBVN6kCaRH0mOCHqRQVdjQoKChAfHwuZLAxxcTEoLi5m2/T09ODpOQJisRR+fgFo3doClpam2LTpR842aFIH0lRUneCEtBxU0JtZUVER4uOPQqEIQ2zsERQWFrJturq6GD7cs1IRt6yyvpOTM/74482TThDSmGqa4IS0TFTQm0FxcTESEuIhl4chJuYwCgpesG06OjoYMmQ4JBIp/P3HoE2bNjVu64svvkRaWgpN6kCa3OsTnNB7reWjgt5ESktLkZh4DDJZGI4cicbz58/YNoFAgMGDh0IkCkJgoBjt2rVTebs0qQNpLvRe0zxU0BtRWVkZ/vvfRMjlYYiOjuQMHiUQCDBw4CCIxUEIDJSgQ4cOaoyUEMJHVNAbqLy8HKdO/RcKRTiiohR48uQJp71/fzeIxUEQiYJgZdVRTVESQrQBFfR6qKioQHJyEmSyMERFyfHo0SNOu4uLK0QiKUQiCTp1slFTlIQQbUMFXUVKpRJnziRDLg9DRIQcubkPOO19+/aDSBQEsTgInTt3UU+QhBCtRgW9BkqlEufPn4VcHgaFQob79+9x2h0cHNnulK5du6kpSkIIeYkK+msYhsHFi+chk4UhIkKG7Oy7nHZ7+17/OxOXokePns0eHw1IRZoLvdc0DxV0vCzily+nsJMl3759i9PevXsPiMVSiMVS2Nv3UlOUhBBSM60t6AzD4MqVdMjlYZDLw5CZ+Ren3da2K1vEe/d2oEmSCSEtntYV9GvXrrJF/M8/b3La3n67CyQSKcTiIPTp05eKOCFEo2hFQf/zz5uQyQ5BoQjHtWtXOW2dOtmwd6f06+dCRZwQorFULuiPHj3CmDFj8O2338LLywt3797F4sWLkZqaivbt22PhwoXw8vJqyljr5K+/MqBQhEMmC8OVK2mcNiurjmwRd3Ud0CxFnGZQJ4Q0NZUL+uLFi5GX9/dX2efMmYPBgwfj559/RlJSEr744gvExcXB0rLqCIHN5datLMjl4VAowpGayh36s337DhCJJBCJpHBzGwgdHR01RUkIIU1DpYK+f/9+GBkZwcrKCgCQkZGBGzduYN++fdDX14eHhwfc3Nwgk8kQHBzcpAG/7u7dO1AoZJDLD+HixQuctrZt2yIwUAyJZCwGDhwEXV3dZo2NEEKaU60FPSsrCzt37sTBgwchlUoBAH/99Resra05ExHb2tri5s2b1W3mjQQCAepzopyb+wB79vyMX389gLNnT3PaLC0tMWaMGGKxFEOGDIWeXsu4TKCrK+A8rvxcFTo6As7/2oBy5j9tyxdo2pxrrHbl5eWYP38+Fi9eDAuLv/t8CwsLYWRkxHmtUCjkzLijijZtTOrcf52bm4vBgwfg6dOn7LLWrVtDKpVi3Lhx8PLyaqHDfJayj8zNjWFpaVqvrVhYmDRWQBqDcuY/bcsXaJqcayzomzdvRq9eveDh4cFZbmRkVKV4FxcX13nW+cePC+p8hp6fXwhdXV2Ym5vD3z8QYnEQPDy8YGBgAAB4/rwEQEnNG1GD/PzC1x4b1Gl9HR0BLCxMkJdXAKWSaeToWibKmf85a1u+QMNzrulksMaCHh0djYcPHyI6OhrAy4mM586di+nTpyM7OxulpaVsIc3MzMTAgQPrFBjDMKioqNMqsLBog6tXM2BhYYxnz4pRUfHyB/Lq/5aqcnwVFUy941Uq67+upqKc+U/b8gWaJucaC/qRI0c4z0eMGIGQkBB4eXkhJiYG69atwz/+8Q/88ccfOH36NJYubZ4ZwXV0dFpM33hzqHzL4+TJU2Bqaq7miAghLVG9q+LGjRuxZMkSDBo0CG3btsXatWvZu2AIIYQ0vzoV9GPHjrGPra2tsX379kYPiBBCSP3Qt2sIIYQnqKATQghPUEEnhBCeoIJOCCE8QQWdEEJ4Qntu5laDyveP+/mJERcXh7t37+LevVwsWbJS5SEKysrK2HXv33+IkJAVLXR4A0KIOlFBbyZbt27CyZMnAQDbtm2GUGiExYtV+yLW+vVr2HW3bv0RhoZCldclhGgP6nJpJpcvX+Y8v3DhnMrrpqRwx3avy7qEEO2hcQU9Pz8PGzeuwfLly5Gfn1f7Cg3c1+bNa7F589oG78vR0ZHz3MWlv8rrOjn1q/e6hBDtQV0uzWT69M9x8+Z1ZGdnw8fHHwsWLFJ53TlzvkR6eiqys7Ph61u3dQkh2oMKejPR19fHyJEjAbycU7QuFzUrrzt58hS6IEoIeSON63IhhBDyZlTQCSGEJ6igE0IIT1BBJ4QQnqCCTgghPEF3uWgAc3MLzJr1JSwtTfHkyQutm3uREKIaOkMnhBCeoDP0GlQeFKuuA2q9vv6tW3fQqVNH6OrqNmHEhBBtRmfoNXg1KFZWVha2bduM7777tt7r79y5HQkJCU0UKSGEUEGvUUMHxXp9/ezs7AbHRAgh1aGCXoOGDor1+vrW1tYNjokQQqqjcX3ozTnZQ+VBseo6oNbr63t6eqNTJ6smiZMQQgANLOjNOdlDQwbUetP65uYWjR4jIYS8onFdLjTZAyGEvJnGFXSa7IEQQt5M47pcaLIHQgh5M40r6DTZAyGEvJnGdbkQQgh5MyrohBDCE1TQCSGEJzSuD705mZtbYMaMueoOgxBCVEJn6IQQwhNU0AkhhCdUKujR0dHw8/ODs7MzAgICEBcXBwDIz8/HzJkz4erqCk9PT4SGhjZpsIQQQqpXax96ZmYmFi1ahB07dsDFxQVJSUn49NNPceLECSxbtgzGxsZISkrC9evXMXXqVDg6OsLe3r45Ym/xqA+eENKcai3otra2OHXqFExMTFBQUIDc3FyYmJjAwMAAcXFxiImJgaGhIfr27YvAwECEhoYiJCREpZ0LBALo1LHTR1dXwFm/8nM+09ERcP7XBpQz/2lbvkDT5qzSXS4mJia4c+cORo8eDYZhsGzZMty+fRt6enqwsbFhX2dra4vY2FiVd96mjQkEgromVco+atXKCJaWpnVcX7NZWJioO4RmRznzn7blCzRNzirftmhlZYXU1FScO3cOM2bMwJQpUyAUCjmvEQqFKC4uVnnnjx8X1PkMPT+/kH387FkRgBd124CG0tERwMLCBHl5BVAqGXWH0ywoZ/7nrG35Ag3PuaaTWJULup7ey5cOGjQIo0ePRlpaWpXiXVxcDGNjY5UDYxgGFRUqvxwAUFHx9w/g5fra8SZ4RamknLWBtuWsbfkCTZNzrefHiYmJ+OijjzjLysrK8Pbbb6O8vBw5OTns8szMTHTv3r1RA3ydubkFZs36EkuXLqUJIwghpJJaC3rv3r2RlpYGmUwGpVKJxMREJCYmYvz48fD29saaNWtQVFSE1NRUREZGYsyYMc0RNyGEkNfUWtDbtWuHrVu3Ys+ePejfvz/Wr1+PH3/8Ed26dcPKlStRXl4ODw8PzJ49G/Pnz4eTk1NzxE0IIeQ1AoZh1NZx9fDh83qtp6srgKWlKZ48eaE1/W6UM+XMR9qWL9DwnNu1M6u2jb76TwghPEEFnRBCeIIKOiGE8AQVdEII4Qkq6IQQwhNU0AkhhCfUetsiIYSQxkNn6IQQwhNU0AkhhCeooBNCCE9QQSeEEJ6ggk4IITxBBZ0QQniCCjohhPAEFXRCCOEJKuiEEMITGlfQr1y5gnfeeQf9+vWDWCzGpUuX1B1Sozt37hzeffdduLq6YuTIkThw4AAAID8/HzNnzoSrqys8PT0RGhqq5kgb36NHjzBo0CAkJCQAAO7evYsPP/wQzs7O8PHxYZfzwf379zFt2jS4uLhg+PDh2LNnDwB+H+cLFy5AKpXCxcUFPj4+iIiIAMDPnFNTUzF06FD2eU05lpaWYtGiRXBzc8PgwYOxZcuW+u2U0SDFxcXMsGHDmH379jGlpaVMaGgoM2TIEKakpETdoTWavLw8ZsCAAYxcLmcqKiqYtLQ0ZsCAAcypU6eYWbNmMfPmzWOKi4uZlJQUxs3Njbl69aq6Q25Un376KWNvb88cO3aMYRiGkUqlzPfff8+UlpYyx48fZ5ydnZnHjx+rOcqGUyqVTFBQELNq1SqmtLSUuXHjBjNgwADm/PnzvD3O5eXljLu7O3P48GGGYRjm7NmzTO/evZk7d+7wKmelUsmEhoYyrq6ujJubG7u8phxXrVrFfPjhh8yzZ8+YzMxMxsvLi4mPj6/zvjXqDD05ORk6Ojp4//33oa+vj3feeQetW7fm1VlbTk4OPDw8IBKJoKOjAwcHBwwcOBAXLlxAXFwcZs+eDUNDQ/Tt2xeBgYG8OJN5Zf/+/TAyMoKVlRUAICMjAzdu3MDMmTOhr68PDw8PuLm5QSaTqTnShktJSUFubi7mzZsHfX199OjRAwcOHECHDh14e5yfPXuGJ0+eoKKiAgzDQCAQQF9fH7q6urzK+dUczNOnT2eXFRQU1JijQqHAtGnTYGZmhi5duuCDDz7AwYMH67xvjSromZmZ6NatG2eZra0tbt68qaaIGl+vXr2wevVq9nl+fj7OnTsHANDT04ONjQ3bxqfcs7KysHPnTixbtoxd9tdff8Ha2hpCoZBdxpec09PT0aNHD6xevRpDhgyBj48PUlJSkJ+fz9vj3Lp1a7z//vuYO3cuHBwcMHHiRISEhODp06e8ynns2LGQy+VwdHRkl926davaHPPz8/Ho0SN07969SltdaVRBLywshJGREWeZUChEcXGxmiJqWs+fP8f06dPZs/TKhQ3gT+7l5eWYP38+Fi9eDAsLC3Y5n493fn4+Tp8+zf6F+a9//QsrV65EYWEhb4+zUqmEUCjE+vXrcenSJWzduhXffvstXrx4wauc27dvD4FAwFlW03EtKioCAM57vb75a1RBNzIyqpJkcXExjI2N1RRR07lz5w4mTJgAc3NzbNq0CcbGxrzNffPmzejVqxc8PDw4y/l8vA0MDGBubo5p06bBwMCAvUi4YcMG3uYcGxuL1NRU+Pr6wsDAAJ6envD09MTGjRt5m/MrNb2XXxX6yu31zV+jCnrXrl2RmZnJWZaZmcn5U4UP0tPTMW7cOAwdOhSbN2+GUChE586dUV5ejpycHPZ1fMk9OjoaUVFR6N+/P/r374+cnBzMnTsXmZmZyM7ORmlpKftavuRsa2uLoqIilJeXs8sqKirQu3dv3h7ne/fucY4l8LIb0cHBgbc5v1LT59fCwgJt2rTh1LY3dS+rpLGu7DaHkpISZujQocyePXvYu1zc3d2ZgoICdYfWaB4+fMi4u7sz27Ztq9L2+eefM3PnzmUKCwvZq+SXLl1SQ5RNy8vLi73LJSgoiPn3v//NlJSUMMePH2f69evH5OTkqDnChisqKmKGDRvGrFq1iikrK2POnz/P9OvXj7l48SJvj/O1a9cYBwcH5vfff2eUSiVz+vRpxtnZmUlNTeVlzsnJyZy7XGrK8V//+hczadIk5unTp+xdLtHR0XXep0YVdIZhmKtXrzLjx49n+vXrx4jFYubixYvqDqlRbdmyhenZsyfTr18/zr+1a9cyT58+ZWbPns0MGDCA8fDwYEJDQ9UdbpOoXNDv3r3LBAcHMy4uLszo0aPZ5XyQlZXFBAcHMwMGDGC8vLyY33//nWEYhtfHOT4+nhGJRIyzszMTEBDAxMbGMgzDz5xfL+g15VhUVMSEhIQw7u7uzKBBg5gtW7bUa580BR0hhPCERvWhE0IIqR4VdEII4Qkq6IQQwhNU0AkhhCeooBNCCE9QQSeEEJ6ggk4IITxBBZ0QQnji/wGl3hUUn1eRaQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x135df9d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import optimize\n",
    "\n",
    "def squared_loss(theta, x=x, y=y, e=e):\n",
    "    dy = y - theta[0] - theta[1] * x\n",
    "    return np.sum(0.5 * (dy / e) ** 2)\n",
    "\n",
    "theta1 = optimize.fmin(squared_loss, [0, 0], disp=False)\n",
    "\n",
    "xfit = np.linspace(0, 100)\n",
    "plt.errorbar(x, y, e, fmt='.k', ecolor='gray')\n",
    "plt.plot(xfit, theta1[0] + theta1[1] * xfit, '-k')\n",
    "plt.title('Maximum Likelihood fit: Squared Loss');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "It's clear on examination that the outliers are exerting a disproportionate influence on the fit. This is due to the nature of the squared loss function. If you have a single outlier that is, say 10 standard deviations away from the fit, its contribution to the loss will out-weigh that of 25 points which are 2 standard deviations away!\n",
    "\n",
    "Clearly the squared loss is overly sensitive to outliers, and this is causing issues with our fit. One way to address this within the frequentist paradigm is to simply adjust the loss function to be more robust."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Frequentist Correction for Outliers: Huber Loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The variety of possible loss functions is quite literally infinite, but one relatively well-motivated option is the [Huber loss](http://en.wikipedia.org/wiki/Huber_loss_function). The Huber loss defines a critical value at which the loss curve transitions from quadratic to linear. Let's create a plot which compares the Huber loss to the standard squared loss for several critical values $c$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UcQn0pxFJowJ8XC1wszflblI2528m0bK+Y+lPEqqt4OB3kUpLvpFqU4L8gVOnjjN//vf4+fnz7bfzmDZtMosXL+fatSvMmTOdr79eSP36Ddi8eT0TJ37Azp07ivfh5OTM1q27UalUT91+REQ4n3wykS+/nEHbth04c+YkU6Z8ytKlv6NQKFi2bAkrV67H0dGJ5ct/5ocfvuHHH3/hl19+xNvbl4ULfyI5OYng4BEEBrYiMLDlM1/PlCmf4uNTm61bd5GcnMSYMSPx9vblrbdGPLODoaWlFevWbcHMzIxNm9aVuC8y8g4dOnQq/r5WLQ+ysrJISkoqTrDC0z04h9qpiWuV9QAvjUgaFSCRSOjcxJWVu29y4EKMSBqlqOxP/pVtyZJf8fb2LXFb795dtX5+t249CAjQVBl977336dWrCwkJ8fz771Z69OhDo0aNAXjttcFs2LCWU6dOYW2t6TvfvXtPjIyeXTl5377dNG/ego4duwDQunU72rbtwO7dO3jttTcpLCxky5bNdOkSxPDho3j33dEAmJqacfHieQ4e3E9gYEs2bvwHaSk9F2JjY7h27QrffLMIhUKBm5s73323GCsr61LH4VmtaPPyclEoHh6Hf/D//HzRSrk0yRm5hISnYCCT0E4HJdCfRiSNCmrl78T6g+HcjE4nJikLV3szfYck6ImT08M/ZAsLC4yNjUlJSSYhIZ7z58+xc+e24vsLCwuJi4srThq2tqX3aElLS33s07iTkzNJSYnY2toxf/73rFmzkvXr12BhYcnIkcH07t2PMWM+4Ndfl7J06SKmTfsvrVq14ZNPPsfG5un7TE1NxdjYBDOzh7/PXl6aVscrV/7O6tW/P/acoKAefPTRp898DQqFgvz8/OLv8/I0yUKbnucvukMXY1EDzes6YGGiv9YMImlUkLHcgNb+Thy8EMPBC7EM6V6n9CcJNdKz2rsCpKY+vGYnIyOd3NxcnJycsbW1Y/DgYYwcGVx8f2xsNHXqeBEREX3/ltIPNTg6OnH16uUSt8XFxWJv70BaWhrGxiZ8880P5Ofnc/DgPmbO/JKWLVsTHx/PkCFvM3bsB8TE3GXOnOn8+utSPv548lP3ZW9vT25uDllZWcWJY8+enZibWzBs2DsMG/ZOqfE+iYeHF1FRkcXfR0VFYmZmhp2d/TOeJRQpVcUVKPR1AvwBcea2Ejy4Qvz41TjyCp7czlOo+dzdPdi/fw/5+XncvHmdY8cOl7h/164d91u/5rFo0UJat26LjY0tPXv24Z9//uLGjeuo1WoOHTrAkCGvERdXtr4sXbt25/z5sxw6tB+lUsmJE8c4evQwQUHdSUiIY8KEsdy4cR25XI6lpRVGRkYoFMasWPErixd/T35+PtbWNshkBlhYPLt9q6OjEwEBTViyZBH5+flER0exaNFCZBW8kKx7955s2bKZiIhwsrOz+PXXJXTr1rPUw2UvuvM3k7iXU4irnSm13fTbelfMNCqBu4MZvq6WhMVkcPJaAp101AxF0K3g4LF8/fVs+vTpTt269ejZsy8ZGQ9L5Ldr14F582YTHx9L8+YtmDx5KgCNGzdl3LgJzJjxBQkJ8Tg5OTFjxhy8vb25evWm1vt3c3Nnzpz5LF78AzNnTsXJyYkvv5yJn5///fjG8fnnk+4fxnJm+vS5mJmZMXHip3z99Wz69+8BaMq7PziRPXHieAICGj/xxPa0abNZsOArXn65FwqFguHDRxIY2Kp8g/fIGMXFxTJp0odkZWXSunU7xo79oELbfBEcOP/wBHhpq96qmmj3+hRlbZV44mo8v/xzDTd7U6aNaKH3H6yuiXacZVNdxis09Crnz59lyJC39RaDNqrLeOnD3cQsvlh+GrmhjAVj22Ki0O6zvmj3Ws01r+uAhakRd5OyuRktGjQJNcPJk8cJCnpJ32EIz7D33F1A02hJ24RRlUTSqCSGBlI6NdbUgdl79q6eoxEE7QwfPgpHR3F9RHWVlVvIyavxAHRtptsS6E8jkkYl6tTEFZlUwvlbSSRniHo6giBUzJGQWAqKVPh72ei00dKziKRRiazM5ATWc0Ctfli6WBAEoTyUKhX77x+aCqomswwQSaPSdW2u+eEevhhLfqFSz9EIglBTXbyVQsq9fBysjGnoU/rFn7oikkYl83GxxMvZguy8Ik7db/ouCIJQVvvOaS787NrMTW91pp5EJI0q8GAqufdsNM/5imZBEKrA3cQsrkelIzeU0bah/upMPYlIGlWgeT2x/FYQhPKrbstsHyWSRhUQy28FQSiv6rjM9lEiaVQRsfy2ZhHtXitPeno67do1p1u39sVf8+bN1ndYNUZ1XGb7qOo173mOPFh+e/JaAgfOx/BqZ9/SnyQIz4Fbt67j5eXNypXr9R1KjaNSqdl/TrNcvzots32USBpVqGtzN05eS+DwpVj6tfNCbvhit7OM+e4bsi+H6GRfpg0b4frB/1XqNkW7V+3avd68eYPateuWZ4hfeBfDkkm5l1ftltk+SiSNKvRg+e3tuHucupZAhwAXfYckPINo91pSedu93rx5g7i4WAYPfoXs7CxatWrLuHETMDd/cgE84aG9Z6vnMttHiaRRxYKaufHLtmvsORtN+0bOL1z120dV9if/yibavT5UkXavZmZmNG3anMGD36KoqJCZM6cyf/5spk2bU+pzX2TR1XiZ7aP0ciI8JCSEdu3alfjez8+PJk2aFH8tWbIEALVazYIFC2jVqhWBgYHMnDkTpbLmXGkd6OeApZkRMUnZXL2dqu9whCr0rHavW7f+RY8enYq/UlNTSjRhqqx2rzduXCc4eASvvNKHf//dCsCYMR8QGNiSpUsX0adPEJ99NrFEl8EneVq7V2tra1au/L3Ea3nwNX/+XAA+/ngywcHjsLCwwMbGlv/8ZwxHjx5+5ixKgF2nowBo18i52i2zfZROI1Or1WzatIm5c+cikz08vn/9+nU6dOjA0qVLH3vO6tWrOXjwIFu3bkUikTB69GjWrFnDsGHDdBl6uRnIpAQ1c2PToQh2nYmmgXf1PE4plE60ey293atKpeLnn3+if/+BODtrDscWFORjYGAguvM9Q1pmPqeuJSCRQLdAd32H80w6/SkuWbKEFStWEBwcXOL2a9euUa9evSc+Z8uWLbz99ts4ODhgb2/P6NGjWb++6ldlJGQncTVR+65qz9KxsStGhlKu3k7lbmJWpWxT0D3R7rX0dq9SqZQrV0JYsmQRubm5pKQks3Tpj/Tq1a9Mr/VFs//8XZQqNU3r2ONgZVzh7RUoC7mQcJm8ovxKiK4knc40XnnlFYKDgzl9+nSJ20NDQzEyMqJLly6oVCp69uzJhAkTMDIyIiIiAl/fh8eZvby8CAsLQ61Wa3V+QCKRUJ4POKtDN3IzLYKRjYbQ3LFx2TfwCEszIzoEuLD37F12n41mVN/6FdpedfTgBPL/nkiuSaRSCTLZ4/HLZJrbx4wZx1dfzaJv3+7UqVOPXr007V5lMgkSCbRv34H582cTFxdLYGBLpkyZhkwmoVmzZowf/3/MnPmg3aszs2bNxdvbm2vXbpXYx5P2/eBfD49afPXVAn788XtmzZqKk5Mz06bNpEGDBgCMGVOy3evMmXOxtDRn0qTPmDt3FgMGPGj32oHhw99FJpMwYcL7BAQ04Z13Hj+xPWPGHObPn8vLL/fC2FjBiBGjaNWqdanjOG3aLBYs+IqBA3sjkUgICurOuHHjn/j6tPU8/H49TX6BkoP3q2L3auVRoXECUKlV/HZ5NSFJ11AZFhFo17Qywiyml3avp06dYvz48Zw6dQqA4OBgWrZsyeuvv05KSgoffPABbdq04aOPPqJ+/fps3ry5eCYSHR1NUFAQISEhyOXyUvelbXL5X7vDDrPs3J/IDeTMCfoEN8uKnZiKS85m9Ny9yKQSfv28OzYWigptTxAqQ0hICKdOnWLUqFH6DuWFte1oBEv/ukw9D2vmje9Q4e39HbqLNSF/Y2pozNcv/Rd708o9JF4tzrY8OOkNYGJiwujRo/nmm2/46KOPUCgU5Oc/nGLl5uZiYGCgVcIASEnJLtdMI9C2KddrhXE06gxfH1nCpy3GozDQbp9PIpdCszr2nL2RxMY9NxjU2afc26qOpFIJVlampKdno1KJIo2lqS7jtWvXXvr06UdqavU+bFpdxquyqVRqNh/QVCIIau5W4Z/DjdRw/gzZAsDwBm9ib2pb7jGzsTF74u16TxoZGRksWbKEsWPHFp9wy8/PL04KPj4+3L59m4CAAABu376Nt7e31ttXq9WUZ7GVTCbhP4FDCE+JIi47gZVXNzDcf3CFlsx2D6zF2RtJ7D9/l16tPJAbPX8X+6lU6nI1sX9R6Xu83nlHM8OoKT8zfY9XZTt3I5Gk9FzsrRQ09rGr0GvLyL/HssurUKOmu0dnGtj5AZU/ZnpfzmBubs6ePXtYtGgRhYWFREZGsmTJEgYOHAhAv379+PXXX4mPjyc5OZmlS5fSv39/ncSmMJAzOuAt5DIjziVe4lDM8Qptz9fNEh8XTa+No5fLdhJUEITnz67TmtVz3Zq7V+h8jVKl5Ncrq8ksyKKOlQ99vLpXVoiP0XvSkEqlLFmyhOvXr9OqVSsGDx5Mjx49ePvttwEYPHgwXbp0YdCgQfTu3ZumTZsyfPhwncXnZOrAkHqDANh8axu3MyIrtL2XWtQCYM+Z6Odqmi0IQtmEx2QQFpOBidyAdo0qds50S8QOwjNuY2lkzvAGg5FJq+4ohl5OhOtSUlJmuZ4nk0mwsTEjNTULpVLN+ptbOHT3GNZyKz4N/AAzo/JVn1Sp1Hy69ATJGXmMfbkhzeral2s71c3/jpfwbGK8yuZ5HK+f/rrM2RtJ9GrlwaBO5T/HeTHpCr9cXoFUIuWDJqPxtfICKj5m9vZPLvui95lGTTHQtzdeFrVIy0/n92t/olKX7+pWqVRCt+aai3d2nYmqzBAFQaghktJzOXczCZlUUqGeGYk5Say8prlubYBPr+KEUZVE0tCSgdSAdxsMxczQlNDUm+y4vbfc22rXyBljuQFhdzMIj80o/QmCIDxX9pyNRq2GFn6OWJuXb1VmgbKAZVdWkafMo7F9Q7q4t6/kKJ9MJI0ysFZY8Y7/m0iQsOPOPq6m3CjXdozlBsWd/Xafji7l0YIgPE9y8go5EqJZCPNSi/KVDFGr1ay78TcxWXE4GNsx1O9VnRVDFUmjjPxs6tDLKwg1av64+iepeWnl2k5Qc3dkUglnbySSmFZzurIJglAxBy7EkF+gxM/DmlqO5SsXfzzuNCfjz2IoNWRkw2EYG+juYmGRNMqhh2dX6tvUJbsoh2VXVlGoKirzNqzN5bTyd0Sthp2nxLkNfRPtXitPfHwcH300nh49OtGnTzcWLpxPYWFh6U98ARQUKtlzRnN0oVcrj3JtIyrzLutvai7ge7PuQFzNdFtGXe8X99VEUomUt/3fYO7p74i8F83mW9t4ve6AMm+nZ0sPjl+O5+jlOPq188LKrPxXnNcE/24IISpcN+Xha/nY0PvVRjrZl1DStGmf4+/fkLlzvyE7O4vx49/j77838eqrb+g7NL07ejmOezmFeDiZU9+z9N4k/yunMIdll1dRpCqirUtLWjo3q4Ion03MNMrJzNCUkQ2HIpPIOBxznDPxF8q8DRc7U5rUsadIqS7+9CFUX4MG9eXYsSPF3y9atJBZs6YWf/+g3WvPnl346KPxxMfHF9936NB+hg17jR49OvHBB+8RFaW53icuLpaXXurIrFlT6dGjE7t2bX9mDGfOnOTdd4fRvXtH3nlnMCdOHC2+b9261Qwc2Jtevboyduworl8PvR9XPOPHB9OjRydee60/P/30HdqstE9IiGfSpAl0796RAQN6snbtKgBWrFhOt27tH/uaN282AAsX/kRw8DgkEgnJyckUFORjaWlV6v6ed0qVqvioQu9WHmU+B6FSq1gRuo6UvFTczV15tbZ+KgeLmUYFeFrUYlDtvqy7+Tdrrm/EzdwFZ1PHMm2jd2sPzt9M4sCFGHq39sBEYVhF0epfdf/kL9q9llTedq8PSgC9//5oLlw4R7NmgXTs2FnrcXxenb6WSHJGHo42JjStU/brs/ZGHeJycij/p1ugAAAgAElEQVQmBsaMbDAMQ5l+3ivETKOC2ru2prljYwpUhfxyeWWZ69d7OVvg52FNXoGS/edjqihKQRtLlvzKzp0HS3xZWFho/fwH7V6NjIx47733uXw55LF2rwYGBrz22mCUSmVxlWd42O5VoXj6Cc1H270aGBiUaPeqUCiK272Ghd1k+PBR/PjjL0DJdq/GxiZs3PhPqQnjQbvXsWM/KNHutXbtulqPx/z537N16y6KioqYP//FbvWqUqvZflIzu+zVslaZS4bcTAtna/hOAN6u/wZ2xjaVHqO2RNKoIIlEwuB6g3AydSQhJ5E11zdqNfV/VK/WmhNie85Gk19Yc1rZCiWJdq9zS2xDLpdjY2PLu++O5tChA6W+vudZSFgKMcnZWJvLad3AqfQnPCI9P4PlV1ejRs1LHl2KCxHqizg8VQnkMiNGNRjG12e/51ziJbytPOnk1lbr59f3sMbTyZw78ZkcDYmr0BWiQtUR7V5Lb/eqVCp55503+fLLWfj61gagsLCwRPJ50ajVav49eQeAlwLdMSil++GjlColyx8UIrT2pY931RUi1JaYaVQSTWHDV4GyFzaUSCT0vj/b2HkqiiJl+UqUCFVLtHstvd2rTCbD29uHZcsWk5OTQ1JSIsuWLaZPH91Upq6ObkanEx5zD1OFAR3uX9SrrS3hOwjPuIOlkQUj/Acjlej/LVv/ETxHmjkG0MmtLUq1pkxxVoH2J1Gb1LHHycaElHt5nA5NqMIohfIKDh5LbGwsffp05/vvv6Fnz74l7m/XrgPz5s2mf/8e5ObmMHnyVAAaN27KuHETmDHjC7p378iyZYuZMWNOmfrCALi5uTNnznz++ONXevTozE8/fceXX87Ez8+fevXqExysafcaFNSORYu+Zfr0uZiZmTFx4qckJyfTv38PBg7sjZ2dXfGJ7IkTx7NixfIn7m/atNmkpCTz8su9+OCD9xg+fCSBga1KjXPixM8wMTHl1Vf7Mnr0cFq1avvME+fPu3/vn8sIau6Owkj7gzsXEy+zL/owUomUdxsMxdyoeszWRJXbpyhvhcgiVRELzy/l9r1I/GzqMCZghNafDo6ExPLb9uu42Jky/d0WSHVUFqAyPI9VSKtSdRmv0NCrnD9/liFD3tZbDNqoLuNVVpHxmUz7/QxyQxnzxrTBzFi7FU+JOUl8deYH8pR5vOLbhy61yt4GVlS5rSE0hQ2HFBc23F6Gwoat/Z2wNpcTm5zNpbDkKoxSEDROnjxOUNBL+g7jubXjlGaW0bGxi9YJo0BZoFmJqcyjiX1DOuuoEKG2RNKoAo8WNtxZhsKGBjJpcZOm7Sciy7wKSxDKavjwUTg6lm01j6CdhLQczlxPRCaV0D1Qu8KEarWatTf+IjY7HgcTO4bosBChtkTSqCJ+NnXo7dWtuLBhSq52hQ07BrhgqjAgPPYe1yPLVwxREAT903zwgzYNnLCx0K6g4PHY05yKP6cpRNhAt4UItSWSRhV6ybML9W01hQ1/1bKwodxIVvypZMuxO1UcoSAIVSE5PZfjV+KRSLQvTBh17y7rb+mvEKG2RNKoQlKJlLfrv4GNwprIzGg23/pHq+d1beaOidyAm9HpYrYhCDXQthORKFVqWtV3wtHGpNTHZxfmsOzKSopURbTTUyFCbYmkUcXMDE0Z2WAoBhIZh2NOaFXY0ERhUDzb2HrsdlWHKAhCJUrOyOXY5TgkEujb1rPUx6vUKlZcW0tKXhq1zF0ZpKdChNoSSUMHPCzceeX+L8Ka6xuJzYov5RkQ1NwNY7kB16PSuRElZhuCUFNsvz/LaFnfESctZhm7Iw9yJeW63gsRakskDR1p79qKQMcmFKgKWXZlJXlFec98vInCkG7NNeVEtopzG4JQI6Rk5HEkJA4J0LeNZ6mPv556i20RuwBNIUJbPRYi1JZIGjoikUh4s94rOJs6kpCTxGotCht2C3THWC4jNDKNm9HpOopUEITy2n5SM8toUd8RZ1vTZz42PT+D366uQY2aHtWgEKG2RNLQoQeFDeUyI84nhnDw7rFnPt5UYUhQM3FuQxBqgtR7eRwJidVqlqFU3S81VJhNXWtfeleDQoTaEklDxxxNHRjq9xoAm8O2EVFKYcNuge4ojGRcu5NG2N2MZz5WEAT92X4ykiKlmkA/B1zsnj3L+Dt8OxEZd7CSWzK8mhQi1FbNifQ50tShEZ3d2qFSq/j1yioyC7Ke+lgzY0OC7p/b2CJmG4JQLaVl5nP4knazjAuJl9kffeR+IcIh1aYQobZE0tCTAb698LLwID0/g9+v/olK/fRy6N0DayE3knH1dirhMWK2IQjVzYNZRrN6DrjaPz0JJOQksSp0PQAv+/bG29JTRxFWHpE09OTRwobX026x/faepz7WzNiQoGZitiEI1VFaZj6HLsYC0O8Zs4wCZQHLLq8kT5lPk/tHG2oikTT0yFphxXD/wUiQsOPOPq6mXH/qY7sHuiM3lHElIpXwWDHbEITqYsepSIqUKprVtcfN4cmzjMcKEdYbVO0KEWpLJA09q2dTm95empUTf1xd+9TChuYmRnRp5grA34cjdBafIAhPl3ovj4MXNLOMZ53LOBZ7ilPx5zCSGjKqwVvVshChtkTSqAZe8uyMv229Ugsb9mzpgbFcxtU7aYSKmlSCoHdbj92mSKmihZ8DtRyf3LQo6t5dNty8X4iw3iu4mNXsUvQiaVQD2hY2NDM2pMf9fhubD4WLfhuCoEfxqTkcDYlHKpEwoP2TW/cWFyJUK2nn2ooWTk11HGXlE0mjmjA1NNGqsGFQc3fMTQwJj73HpbAUHUcpCMIDfx+JQKVW066R0xNrTJUsROhW7QsRakskjWrEw8KdQXWeXdjQWG5A79aeAGw+HI5KzDYEQeeiEjI5HZqIgUxCv7ZeT3xMyUKEQzGUGug4yqpRpqSxf/9+kpKSAFi9ejVDhw5l7ty55OfnV0lwL6J2Lq0IdGz6zMKGnZu4YG0u525SNqdDE/QQpSC82P66vxilcxO3J3blq4mFCLWlddL48ccfmThxIjExMZw+fZpZs2bh4+PDkSNHmDNnTlXG+ELRFDYc+MzChoYGMvq303y6+fuI5kScIAi6EXY3g0vhKcgNZfRu/XhXvhKFCD271phChNrSOmls3LiRhQsX0rhxY7Zu3UqzZs2YNm0ac+bMYefOnVUZ4wvnQWFDhUz+1MKGbRo44WhtTGKapuGLIAhVT61Ws+lQOKCpC2dhalTi/kcLEdazrk1vr276CLNKaZ00UlNTqVOnDgAHDx6kU6dOAFhaWlJQUFAlwb3IHE0dGOL3KvDkwoYGMmnxio2tx+5QWKTUeYyC8KK5eieVG9HpmCoM6NHC/bH7Hy1E+I7/mzWqEKG2tH5FtWvXZu3ataxatYrk5GS6du1KXl4eS5Yswd/fvypjfGE1dWhEF/f2Ty1sGOjngJu9GWmZ+Rw4H6OnKAXhxaCZZWjOZfRs5YGJomSHvfOJIY8UIhxa4woRakvrpPHJJ5+wdu1aZs6cyejRo/H09GTu3LkcPXqUyZMnl2mnISEhtGv3sO5KRkYGY8eOpVmzZnTq1IkNGzYU31dQUMDkyZNp0aIFbdq0YfHixWXaV003wKcX3paeTyxsKJVIGNhRM9vYdiKS3PwnXxQoCELFnb+ZRGR8JpamRnRt6lbivoScJFaHat63Bvr2wdvy8XMdzwutk0ZgYCAnTpzg1KlTTJgwAYBx48Zx4MAB/Py0O9GjVqvZuHEjI0aMoLCwsPj2KVOmYGJiwvHjx/n++++ZP38+169r6jB9++23xMbGsm/fPtasWcOGDRvYv39/WV5jjSaTyjTlkw3NnljYMMDHFh9XC7JyC9l9JlpPUQrC802pUrH5/oqpPm08kRvJiu/Lf6QQYVOHRnRya6uvMHWiTAfcbt26Vfz//fv3M2/ePP7880+tr0xesmQJK1asIDg4uPi27Oxs9u7dy/jx45HL5TRq1Ig+ffoUzza2bt3K6NGjMTc3x9PTk6FDh7J+/fqyhF3jPWjU8qTChhKJhEEdfQDYeSqKjCyx/FkQKtuRkDjiUnKws1TQsbFL8e2aQoSbic2Ox9HEvkYXItSW1lebrFu3jmnTpvH7779jZmbG+PHjadWqFUuXLiU5Obl49vEsr7zyCsHBwZw+fbr4tsjISAwMDHB3f3hSycvLi927d5ORkUFycjK+vr4l7lu9erW2YSORSJCW41yUVCop8a++1bevTT/fl9gStpM/rq1lcssPsTW21tznZUOT2nZcuJXMlmO3Gd5L90v8qtt4VXdivMpGn+OVm1/EliOalgSvdfEtMcs4fPckp+PPYyQ15D8Bb2EqN9Z5fE9TVWOmddJYvnw5c+bMoUWLFsycOZN69eqxbNkyTp8+zcSJE7VKGg4ODo/dlpOTg0JR8uIYhUJBXl4eubm5ABgbGz92n7ZsbU0rlPmtrJ7dtlGX3rTuS3RODOdjL7P86mqmd52IoUxzMm7Uy40YN/8Ahy/GMiioLh5OFnqJsTqNV00gxqts9DFeq3aGkpFdQN1a1vRo6138fhKeGsn6G1sBGB04lIa1fJ+1Gb2p7DHTOmnExcXRokULQLPk9uWXXwbA2dmZrKyntystjbGx8WNJIC8vDxMTk+JkkpeXh5mZWYn7tJWSkl3umYaVlSnp6dmoVNWnVMeQOoOITL1LeFokS0+uYbDfKwCYGkro3MSFfedi+OWvEP7v9cY6jau6jld1JcarbPQ1Xqn38vjrQBgAgzp5k5aWDWgKEc47uZQiVREd3Frjb1Gf1NTyvw9WhYqOmY3Nk1d/aZ00atWqxYEDB3BycuLu3bt06dIF0Fz05+PjU+aAHvDw8KCoqIjY2FhcXDTHCm/fvo2vry9WVlbY2tpy+/Zt7Ozsiu8ry/7UajXKClzCoFKpUSqrzx+1QmrMyAbDWHDuRw7fPYmXhWdx5cy+bbw4djmeS2EpXA5Pob6n7ksXVLfxqu7EeJWNrsdr06EICoo0DZZ8XCxRKtWo1CqWX/6T1Lw0PMzdGejbt1r/DCt7zLT+DD5+/Hhmz57N2LFj6du3L35+fsycOZMVK1YwceLEcgdgZmZG165dWbBgAbm5uYSEhLBt2zb69u0LQL9+/fjhhx9IT0/nzp07rFq1iv79+5d7f8+DWhZuvFpHMwZrrm8qLmxoYWpUXNZg/f4wUcxQECogOjGLYyFxyKQSBnV6+EF1d+QBrqZcx9TAhHefo0KE2tI6aXTv3p3Dhw+zefNm5s2bB8Cbb77Jvn37aN26dYWCmDFjBkVFRXTs2JHx48fz8ccfExAQAMCHH36Ip6cnPXv2ZPDgwbz22mv07NmzQvt7HrR1aUlLp2YUqgr55coKcu8XNuzW3B1rczlRiVmcuPJ4lVxBELSz/kAYaqBzE1ccrTWHxDWFCHcjQcLb/m8UL0Z5kUjUZejko1Kp2LdvH+Hh4ahUKry9vencuTNyubwqY6yQpKTMcj1PJpNgY2NGampWtZ16FigLmHd2EbHZ8TSxb8i7DYYikUg4fiWOZdtCsTaXM/s/rZAbykrfWAXVhPGqTsR4lY2ux+tKRArfrL+EsdyAuaNbYW5iRHp+BnNOLySrMJuenl3p4/1SlcdRERUdM3v7J3ci1HqmERMTQ79+/Zg0aRK7d+9m165dfPrpp/Tr14+EBFGeWx+MZEaMbKgpbHgh6TIH7h4FoJW/E7UcNeVF9ogL/gShTFQqNevun/zu08YDcxOj+4UIVxUXIuz1HBYi1JbWSWPmzJk4Ojpy4MABNm/ezJYtW9i/fz+urq7Mnj27KmMUnsHRxJ6hfq8B8FfYv4Sn30EqkfB6Z83yv39PRpKRLQpKCoK2jl6OIyYpG1sLBUHNNOVC/gr/l4iMyOe6EKG2tH7lJ0+eZNKkSVhZWRXfZmNjw6RJkzh27PHS3YLuNHFo+FhhQz9PGwJ8bMkvULLl6G19hygINUJeQRF/HdGUC3mlkzeGBjLOJ4ZwIProc1+IUFtaJw0zMzNycnIeuz0nJwdpeS6EECrVAJ9e+Fh6klFwj9+urkGlVvFqZ1+kEgmHLsYQlVC+czuC8CL590QkGVkFeDmb08LPkYTsRFaFasoWPe+FCLWl9bt9165dmTZtWnEhQYBr164xbdo0unbtWiXBCdqTSWWMuF/Y8EZaGP9G7MbFzpQuzVxRq2HNnpta1wgThBdRQloOu05HATC4W537KxNXkq8seCEKEWpL66QxceJELC0tGTBgAI0aNaJRo0YMHDgQNze3MpdGrwmyQi5xd+NmlPdLmdQEVnJLRjTQFDbcGbmfK8mhDGjnhbmJITfvZnBK9BMXhKf6c+8tipRq2jZ0wtvZgj+vbyYuOwFHE4caV4gwPzqaxI0byE9JrfRtP/OqlLCwsBLfT5kyBZVKxe7du7G0tKRly5ZIpVISEhIwN3/y8qyaKmXHdnKuX8fg3x04DnsH04aN9B2SVupY+9LX+yW2RmgKG34a+AGvdPTh9x3XWb8/jMa+diiMXqyLkQShNJfCkgkJT8FYLmNQJ1+Oxp7kTIKmEOHIBkNRGChK30g1oCosJPXfraTu2A5KJVaebhg1r9h1dP/rme8effr0QSKRFB/WeJBpH/1erVYjkUgIDQ2t1MD0zWnY2yQsX0Z2eDgx332Dees2OLw+GJlZ9T8J1s2jExEZkVxJCWXZlZV82OQ9Dl0053ZcJtuOR5a4ulUQXnSFRSr+3Kdp+9CvrRfpygQ23tQUIhxcbxAuZk76DE9rueFhJPy+nIK4WACsuwbh0Kkj6VmVu3rymUlj3759lbqzmkTu4kLAvDmErd1E0l+byTxxnJwrV3AYMhSzZoHVeqoqlUh5u/7rzD3zPVGZMWwO+4fB3YKYteIcu05H0b6RM4422hd9FITn2e4zUSSm5eJsa0KrRjbMP/8DRWolHVzbEOjURN/hlUqVl0fy35tI37cX1GoMnZxwensEZvXqIjUyAnSYNFxdXSt1ZzWNRCbDtmcvTAKakPDHb+TevEHckp8wbdIUxyHDMLCqviUETAxNGNlwKAvO/cTR2FN4W3rSrqEzRy/H8ee+W3z4aoC+QxQEvUvLzGfb8UgA3gyqzaob6zSFCC3cGVi7j56jK132taskrPiNouRkkEqx6dkbm779kBoaVdk+xVpZLRg5OuH20Sc4DH0LqUJB9oXz3JkymYyjh6v1iqRa5m68VltT2PDPG5tp28IUY7mMkPAULoYl6zk6QdC/9QfCyC9U0qyOPdFc5FrKDUwNTRhZzQsRKrOzif/9V2K+mUdRcjJy91rU+u8X2A0cVKUJA0TS0JpEKsWqUxc8ps/CtFEAqtxcEn5fTsw38ylMStJ3eE/VxqVFcWHDtWFr6dVGM3tcu/cWhUUqPUcnCPpzIyqNU9cSMDSQ0ry5hH9vawoRvlP/TWwU1fcoQub5c9z5YjL3jh5BYmCA7cuvUOu/X6Dw8NTJ/kXSKCNDG1tc3v8Qp5H/QWpmRk7oVe58+V/S9u5Grap+b8ISiYQ36r6Mq5kzibnJxBgfx9nOhMT0XHafidJ3eIKgF0qVitV7NCe/u7S0ZXPkJtSo6enZlfq2dfUc3ZMVZWQQu+RH4n76AWVGBgofXzy+nI5t775IDHQ3KxJJoxwkEgkWrdrgOX025i1aoi4oIGntGqLnziI/Nkbf4T3GSGakWTYoU3Ap+Qr+zdMB+Of4HZIzas51KIJQWQ6cj+FuUhY2FkZEKQ6RVZiNn00denoF6Tu0x6jVau6dOMadLyaTdfYMErkc+8FDcf9kMkbOLjqPRySNCjCwsMD5P+/hMu4DZJZW5EWEEzX9S1K2bUVdVKTv8EpwMLFnmN+rAJxIO0h9fygoVLFqt7hSXHixpN7LY9NhTX0p7+Yx3MmMwlpuxTv1q18hwsKUFGK++4b4X39BlZ2NSX1/PKfNxLpLEBI9lW+qvmd6ahCzxk0wrlOHpA3ruHfkMCl/bybz7Bmc3hmBwtNL3+EVa+zQkK7uHdgXfZhkq2MYm7YkJDyFszeSCKznoO/wBEEnVu+5SX6BEl//bK5mnUMmkfFug6GYGZnqO7RiapWKjIP7Sdq0EXV+HlITE+xfexOLtu30vty/eqXVGkxmYorT2yNwmzgJQ3t7Cu5GEzVrOkkb1qEqqD6lyfv79MTH0pPMwkzsA64DatbsuUlOXqG+QxOEKnf+ZhIXbiWjMM8lyfwUAANr98HLspaeI3uoID6Ou/PmkrhmFer8PMyaNsNzxmws27XXe8IAkTQqnYlffTymzsS6m6arV9quHUROnULOjeulPFM3igsbGpmRVHQXe78oMrIL2HQoQt+hCUKVys0vYvWemyAtwsL/MgWqApo5BNDRtY2+QwNArVSSuuNfIqdOIffWTWQWFji/NxaXMe9jYGlV+gZ0RCSNKiCVy7F//U3cP/scIxcXChMTuDtvLgkr/6gWBRCt5JaM8B+CBAlZ5qEYWCdx8EIMYTEZ+g5NEKrMX4cjSMvMw9rvJpmqVJxMHBhcTQoR5kVFEjVrOsmbNqAuKsKiTVvNQptmgfoO7TEiaVQhY28fak2Zhk3f/iCTkXHoAJFf/JeskEv6Do061j708+4BgHHty2CUwx87r1OkrH7LhgWhom7H3WPfubsYOESTZxqFkcyIUQ2HoTCQ6zUuVWEByX9tImrWdPKjIjGwscX1w4k4jRhVbevciaRRxaSGhtj1fxmPKVORe3pRlJZK7PffErdsKcpM/TZGCvLoSEM7P4oowKReCDHJ94r7CQjC80KpUvHHjutgmo6Rp+Yw8ZB6g3AyddRrXLlht4ia9iWp//4DKhVWXbriOX0mpg0a6jWu0oikoSNyN3dqffY5dq++jsTQkMyTJ7jzxWQyz5zW25JXqUTKW36vY6uwQaVIx9AjlK3H7pCY9niHRkGoqfacuUtUairGdS6hRkVHtzY0d2yst3hUeXkk/rma6K9mUxAfh6GTE+6TPsNh8DCkCmO9xaUtkTR0SCKTYfNSTzymzsS4Tl2UmZnELf2J2B+/pyg9TS8xPShsaCA1wMDhLirLaFbsuiGu3RCeC8npufx9NBwj7xDUhrl4WLjzsq/+ChFmX73Cnamfk75vD0gk2PTqg8eX0zGuXUdvMZWVSBp6YOToqCmAOOxtTQHEixc0BRCPHNLLm/WjhQ2NvK4SmhDF0ctxOo9DECqTWq3mj103UNnfQmaVrNdChMrsbOJ/+5WYb+drCgzW8qDW51/qpMBgZRMX9+mJRCrFqmNnTBsGkLjqD7JDLpHwx2/cO3USx7eHY2Sv24vt2ri0IDzjDqfiz2FU+wJrD5ji72mDjUXN6FgmCP/r0MVYQlNuIq8bptdChJnnz5G4egXKjAxNgcF+A7Du3kOn9aIqk5hp6JmhjY2mAOKoYGRm5uReDyXyy89J27NLpwUQiwsbmjojVeSgdL3E8h2h4jCVUCMlpeey7shljHwugQS9FCIsysggdvGi4gKDxrXr4DF1Bja9+tTYhAEiaVQLEokEi5at8JgxC/OWrTQFENf9SfTcmeTH6K4AopHMiJENhyKXyZHZJHAz9zyHL8XqbP+CUBlUajXLt18Bz3NIDAt1XohQrVZz7/gx7kyZTNa5s0jkChwGD8Xt408xcnLWWRxVRSSNasTA3ALnUcG4jPsAA2tr8iIiiJz+BSn/bNFZAUQHE3ve8ntNE4/7TdaeOk1yuv4vSBQEbR04H0MEp5CaZWBpZKnTQoSFKcnELFxA/PJfUOVkY+LfAM/pM7HSY4HByvZ8vIrnjFnjJnhMm4Vlx06gVJKy5S8iZ0wl77ZuSn00dmhIF/f2SCRqJB7nWbbrAipxmEqoARLScth48TAGTlFIkTKq4TCdFCJUq1Sk79/LnS8+J+fqFaSmpji9OwrXDydiaGtX5fvXJZE0qimZiQmOw97B7aNPMLR3oCDmLlGzZ2gKIObnV/n+B/j0wtPcA4lRPnfkh9l/PrrK9ykIFaFSqVmy6xSSWpcBeKVOX50UIiyIjyP66zkPCww2D8Rz+mwsWretFiVKKptIGtWcST0/PKbOwPolTcmPtF07iJz2RZUXQJRJZYxqNBRjqQkyi1Q23dghLvoTqrUdZ8KJNz+MRKYkwLZRlRciVBcVkbp9G5FTp5AXdguZpSXOY97HJXgsBpaWVbpvfRJJowaQyuXYv/oG7p9NwcjVTWcFEK3klvwnYBioJUidwvlx715xmEqolmKTs9gW/Q9S42ysDGx5y//VKv2UnxcVSdTsGSRv3qgpMNi2vabAYNNmVbbP6kIkjRrE2NsbjylTse3/8v8UQLxYZfusY+1DD49uACRZnuTvk1erbF+CUB5FShU/HNqG1CYOqdqA95u9U2WFCFWFBSRv3kjUzGmaAoN2drj+38c4DX8XmWn1aeJUlWruYuEXlMTAANu+/TFr2oyE35eTdzuC2O8XYt6yNQ5vDEZmbl7p++zt04XQxAgi88LYk/w3jWJd8HWxqfT9CEJ5rDh8igzLC0iAN+u+UmWFCHNv3SL+j18pjI8HiQSroG7YDXgFqeLFugBWzDRqKLmrG+6ffY79a28iMTIi89QJ7kyZzL3TJyv9gjypRMq4wKHI1eZITe+x6NRa8gqqVw904cV0PjyGs3k7kEjVBFg2o41b5R8eUuXlkrhmJdFfz6YwPh4jZxfcP/0vDm8MeeESBoikUaNJpFKsu7+kKYBYzw9lVibxPy8h9sfvKUyr3AKIJoYmjGv6DqikFFre4fv92yt1+4JQVunZeSy/+icSeR6WEgdGNHml0veRfeUyd774nPT9+0AqxaZ3X2p9MQ1jH99K31dNIZLGc8DIwQG3iZNweOsdpMbGZF+8QOQXk0k/fLBSZx3e1u70cu8NwB3ZcXZculxp2xaEslCr1XxzYCNqs0SkSiMmtByBQSUWIlRmZRG//BdiFi6gKDUFeS0PPD7/EoJCj1YAACAASURBVLuXX0FqaFhp+6mJxDmNpziy+xZREal417WjbkMnLK1N9B3SM0kkEqw6dHpYAPHSRRJX/E7m6VM4vjUcI4fKKYDYq047riWFc6fgGttiN+Pv5kYtW90XgRNebGtOHSfZOASJGobWewN7k8o7x5Z57gyJq1eivHdPcw6x/8uaAoMyWaXto6qo1Wru3kkj9FIccXczGDSsGRY2lXsITaJ+zivSJSWVrzveoZ03uHbxYXlwl1pW+AU4413HDgPD6v3Lo1aryTxziqQ1q1FmZSIxMsJuwECsgrpXSimD/KICPjuwgHxZGoocV+b2GIdCboCNjRmpqVkolc/1r1SlkMkkYrzK4NHxuhQZzU/XFiMxKKSJeRtGBg6olH0UpaeTuGYlWefPAWBcuw6Ob4/AyMmpUrZflbLu5XE9JJ7rIXFk3tNc/CuRSBjyn5ZY2RmX63fM3v7Ji2pE0ngKqRSyMwo4eSSCsGuJFBVpKs4ayQ2o4++IX4Azdo7Vs4fvA8rMTBLXribz1EkAFF7eOL4zArmrW4W3fSc1nnnnvgdZEb6S1nwUNFC8CZaBSBpl82C8ouNSmLR7AUpFGpYqV2Z2fb/CdaU0BQaPkrTuT1Q5OUjkCuxfGYRlpy7Vul6UUqkiMiyF0EtxREWkFt9ubqnAr5ET9Rs7U8vTrty/Y9U+aSxbtoyFCxdi+Mjxwl9++YXatWszefJkTp48ibm5OWPHjuXVV1/VervlTRqP/lHnZBcSFppI6KU4kuIfbs/eyQy/AGd8/RyRK6rvkb6sixdIXL2CorQ0kMmw7d23Usoz7wg9xba4TajVEga5D+H1tm3Fm6CWRNIomwfj9f6aH0iQXUNaaMK09v+HjYlFhbZbmJxEworfybmmuf7IpEFDHIe9Xa3rRaWlZBN6KZ4bV+LJyykEQCqT4F3HDr8AZ1w9rJFIJBX+HXta0qg273ShoaFMmDCBd999t8Tt48ePx8TEhOPHj3Pjxg1GjRpFw4YNqVevns5ikysM8G/ign8TF5ITMrkeEs+NKwkkxWeRFH+L4/vC8alnj1+AM05ultWu3oxZ4yYY16lL8qb1ZBw6SMrWv8k8dxbHt0dg7O1d7u329GvJ5YQwIlWX2HR7A819fbE2fDEucBJ0b8mB7STIrqFWSRha980KJQy1SkX6gX2aK7rz85GamuLwxmDMW7Wpdn+/AIUFSsKvJxIaEk/83Yzi263tTPALcKaOvyPGJrrpAFhtZhq9evXi888/p02bh/VisrOzCQwMZNeuXbi7uwMwY8YMgP9v77zDo6zSPnzPJJMeSCENCCWBdBJKqIIg0hSQD4kiKCigiI0t7q66fiwW0F1WVz9ZRUWQpiiIZdWlSBERpIiaBEghBZKQ3ggpM5OZOd8fEyYJSWASkswkOfd15VLOvPPmvL/rZH5zznnO87BixQqz7ltYWE5LZphKpQI3N2dKSyswGBpKpKvWk5pUyLnfsrl0sdTU7ubpRFiUHyGDfHFysb4yjhWJCeR8uJHq/HxjjeIpU/GafTdK+5adoK3W6fjz3jdQ2+Vjr+3Bmql/xN62a0eXmMONxpekPqcunOeDpA9QKA1EO0/k4TF3tPhemuxscj7cQFVKCgCuw0fge/8DVpcvSghBfs4Vzv2WQ/LZPKq1egBUdjYMDPMmbLAfPj27NWlyNzvGPDwaX363CtOoqqpi2LBh3HrrrcTHx9OtWzeWLFlCWFgY9913H3FxcaZrt23bxr59+9iyZYtZ9xZCtPk3h+LCCn49mUHsqUzKazahlEoFQeE+DBnZh8Bgb5RK6/n2otdoyPj4E7L/8w0YDDj4+jLgycfoPiiiRffLLCrkT7tXI1RqeikieOPeJ1q5x5KuTG5pKb/7ZhVCVYEPwbx17+9a9Ddt0Om49MVXZH6yA6HToXJ3I/DRpXiOHtkGvW45VZVa4k9f4tcTGeTllJnae/V1Z+jIPoQP7omdveUWiazCNDIzM3nuued45JFHGD16NHFxcSxbtoxFixaxefNmTp48abr2s88+Y8eOHezYscOse7fVTKMxDAYDF1OKOfdbDhdSikxnJFxc7QmN8iU0yo9ubo7N70wbUZWWRs6HG9BkZQHgNn4C3vfOxcap+eHFx9IS2Hx+EwqlgTHdprFw5O2t3d1OhZxpmIdOr+cve96i0i4bVbU7/5j8NE6q5s+K1Rcvkr3xAzQZGQB0H3crPnPvs5p8UUIILl0s5dxvOaQmFqDXGwNvHBxVBA/yIWxwTzy9mtfXTj3TaIyXX36ZtLQ0Tp8+3WCmsX//fjZt2mTWfVpjI7wlm0gVVzQkncklITaHslK1qb13P3dCo/zoP7AHNraWj8wQOh3Fu7+l6Jv/gF6Prbs73g88iEvU4Gbdx8ZGwdbTBzhavAdhUPJQ4GJG9A9qo153fORGuHm8duhT0sVp0Kl46ba/4O3g1iy9DNVair/+D8V7/gsGA7Y9euCzcBHOYeFt2GvzqbiiITHeGCpb93PCv7/xc6LfgJZ/TnTqjfCzZ89y9OhRli5damrTaDT4+fmh0+nIzs6mZ8+eAKSnpzNggPUf4Xd2tWfo6L4MGdWH7IxSEuJySEssIOtCCVkXSnBwtCUo3Dj78GjmN4jWpDYBYjR5mzegTksje+2buI4Yhde8+di6mr/ZuHzSXSRvT6PAJpktSR/Tz/MPeHezrnViScfhq7jjpIvTCAH/02cOIT17U1xcbvb7q84nk7tpI9V5VxMMTjGe6G7h/l1rYTAYuJhabAyVTS3i6td2Z1d7QiJ9CRnka1UrEtdiFTON9PR0Zs2axZo1a5gyZQonTpzg8ccfZ9u2bbz77rvY2dmxatUqzp8/zyOPPML7779PVFSUWfe21EyjMTTqapLP5pEQm0NRfoWp3adnt5rQXS9UdpbzcWEwULr/Owq/3IXQarFxccVr3v24jhh5wzXk2jj6Qp757l/o7Etw1Prx98nLse0AJ2nbGznTuD7ncjJ5+8w6sNERrBrFHybMMVsvg7qKgl2fcfnQAQDs/Hri89Bii+eLulxSSUJcLknxuVSWawHjElK/gZ6ERvnRu59Hq+59ttVMwypMA+DgwYO88cYbZGZm4uPjwx/+8AemTZtGaWkpK1eu5KeffsLJyYknn3ySmJgYs+9rTaZxFSEEhXnlnPstm/Pn8utFRQwI9SYk0ve6URFtjbYgn/wtm6hMOAeAc2QU3g88iMqj6VQNdfVKzs3hX7/+G2y19FMM4c+3zWuvrncYpGk0zeWqClYcfgO9XRmuWn9emfIEKpWNWXpVnIknb8smdMVFYGODxx3T8Zg+02L5onTVetKSC0mIzSE7o06UpYcjIVF+BEf44uTcNlGWnd402gprNI26VGv1pCYVkBCbY/H467oIISj78QcKdnyCoaoKpaMjPWLm0n3crY2ekr1Wr70Jv/BV9icoFDCm2zTuj57Y7s9gzUjTaBydXs9fv1tLhV02Sq0LL437I+7OLjfUS19eTsGO7ZQdOwqAfd9++D60GHv/tq8R3hiFeVdIiM0l+WweWo2xjICtrZLAUG9CI33b5TyXNI0WYu2mUZeSogpj/pj4+ic9+w/sUTN9dW/32YeutIS8bVuo+O1XAByDQ4wJEH3qF7ppTK/3j31LrPowwqDgnj73c1tQZLv23ZqRptE4q/ZvIkd5DnQqnhi0jDA/4/ms6+l15eeaBINXylCoVMYEg5OntnuCQY1ax/lzeSTG5VCQW7v34uXrWrP87N2umSOkabSQjmQaV6mbUyYzvdi0UebazZ6QSD9CIn1x6dZ+xV+EEJSfOkn+9m3orxgTIJr+MGtmHU3ptWr/ZnKUZxt8CHR1pGk05L1j3xCn/gFhUBDjP5+JwbX7lo3pZQ0JBoUQ5GRdJiHWGOhSN0ddcIQPIZGWy1EnTaOFdETTqEt5mdoYkhdbm70SoE+AB6FRfvQd4ImNTfuE7urLy40JEI//BIB9v/74LlqCfa/eTeplXG74NxV2l1BonVkx5vf4yIgqqxlf1sJ/4o+zJ//zJpcz6+ql0xkoO/ojBTuMCQaVDg70iLmX7rdOaLcEg5UVWpLic0mIy+FycZWpvVdfN0IirSMbtjSNFtLRTeMqxsM/xjz5acmFGGr65OCkIjjCl9AoX9w92yd0tzwulvytm9GVFBs3G++cgdfMmfTwcW9Ur8tVFfzt+/9DZ1+KnaYHr9z+exztrC/FSntibePLkpy6kMyH5z9EYaMnQDmMpyfMbXDNVb1yk9PJ+fBDU4JB50GReC94EJWHZ5v302AQZKYbQ2UvphSZDsw5u9gRPMiXkEg/urtbT6isNI0W0llMoy7qqmqSz+RxLjabksJKU7tv7+6ERvkRGOyFyq5tv+Xoq6oo3LWTy98fBMC+Vy+Cf/8U1T38GtXrYlEBa35eCyo1broAXp60FKUVp51ua6x5fLUn6YV5vHb6bVCpcdcF8FIT40KpEGh+OsKFrR8ZEwy6uBgTDI4c3eb7fGWlVaa9xoorV2tVQN8BxlDZPgEeVjmWpWm0kM5oGle5mtAsITaHlIT8BgnNQqP88PJ1bdM/qsrkJPI2b6Q6L89YQ3nyFDzumt3oAapTF87z4fmN1/1G2VXoCOOrrak7A7XXeLH69t81OgPVZGeTv3kjVam1CQa95j2AbbebS4t+PfQ6A+nnjaGyWRdKTO3d3BwIjfIjeJAvzi6WPSR4I6RptJDObBp1qdbqSEkoICEuh7xLtUnOPL2dTaG79g5tE6tu0Gop+fpLivbuAYMBlZcXPg8uxikktMG1X8UfZ2/N2vUQxwk8PPrONumTtdPRxldrU6lVs+LA26jt85rc6xI6HcV7/kvxN/9B6HTYeXjg/cACnCKHtFm/igrKSaypVaFRG0NlbWyVBAYbSx/4+Vtf6YOmkKbRQrqKadSluKCChLgcks/koq6qGfg2CgJqBn7PPm6tPvBtbBSoinJJ+r9/o8nMBKD7rePpEdMwAeKG43v4pfIgQsAt3bvmGY6OPL5uFk11NX87sI5yuyyotueJyKUNourUFy6Qu2kD2izjWHIbP57gpUso04pW10ur0ZGSaCyylp9d+3nRw9tYZG1guHebfeFqS6RptJCuaBpXuTrFTozLITO9kSl2hC/Orq0zxb6qV1F+KQXffmv6dmjj5obPAw/iMrj+t8O1R74gsfonhFAwqccs7o4a08SdOyedYXy1BJ1Bz8r96ym1TQOdisUhixnWJ9D0ukGrpeg/X1Kyr86sdeEiXCPCW1UvIQR52WWmpV1d9dVQWRsGhvmYlnY7MtI0WkhXNo26lJVW1WTTrL+Z1yfQuJnXN/DmNvOu1UuTfYm8TRtRp6UC4DpiJF7z7q+XAHHNoe1cFL8iDAru6jmXaWFDb+4hOxCdbXyZg8Fg4OUDm8i3SUTobZgfsICxgWGm1+vtj11NMPg/xgJhraVXVaWW5DN5JMTl1Asi8asJIgkI8UJl4VDZ1kKaRguRplEfg0GQdcFY86Nu2KBTTdhgaKQv3d2bX0+jMb2EwUDpwf3GkppabYOIF4PBwOqDW8hVnkPobbiv/wPcOsA6Ula3NZ11fF2Pvx/8iExiEQYls3vfx+QQY/r9ayPx7Hr2xOehJTgG1M5AbkYvIQRZF4zh6unJhaYx7+ikMoXKuns2f8xbO9I0Wog0jaaprNCSXFPzo7TOAaWefdyM37qacUDpenpVFxSQt+XDaxIgLkTl4YnOoOfF/R9QbJsKOhWLgh8iuu/A1ntIK6UrjK+6/N8Pu0jWnUAYFEz1mc2sQaOAmjM/2zajK6498+Nx54wGCQZbold5mdoYKhtXezBWoTAejA2JbN+DsZZAmkYLkaZxY4QQ5NakQki9JhVCULhxffdGqRBupJcQgrKjRyj4dLsxAWKdU7zVBj1/2/8eV+wyQGfHI6GLGewf0CbPai10pfH17tGvidccQQi41W069w0bj/7KFfI//bh+doEHF2Pv33iaGXP1qpuCJyOt2NTu2t2B0Ehfgge1bwoeSyJNo4VI02geGrWOlARjJElBbq12Xr4uNUnXfBpNumauXg0SIAYF4/PgIvTuHqw4+G+q7HJBp2LhwAcZ2Ykr/3WV8fXWD5+TpDsOwDCniSwaOZXyn0+R//FWYx4zMxMM3kivkqIKEmpCZesm+wwI6kFIpGWSfVoaaRotRJpGy2kyvXOIMXS3bnrn5uglhKD89CnyP9pWLzOpatx4Xjqynkq7bNDbMrff/dw6sHPucXT28WUwGHj98KdcEL8iBEQ7387CkBGNfGFY3CBjcmM0ple1Vk9qYj4JcbkNygqERfUkKMIHB8eOFyrbWkjTaCHSNG6e6xWSCY3yIyjCF9du9s3WS19eblyi+OkYYFyicL9/Aa8m/5cyVQZCb8Ps3vcwObTzRVV15vFlMBh45dBWchRnEULB2G5Tma62qa3N4uBAj3vm0n3ceLMTDJpCuouukHvJGCp7bQGzwBAvwgb3xNuvbbMgdBSkabQQaRqti6lkZVwulRV1S1b2YOS4/rh7OdHcEVURH0fe1k2mzdDuU+/gHccCCu3TEQYld/jMZuagkW3wNJajs44vnV7Pywc/pNAmGWFQME01gaE/xzerCmRjVGt1ZKWV8vOxCxTm19aq8OnVjdBIy5dKtkakabQQaRptg8Fg4GJqMYmxOVxMLTIZhYurfU0Yoy/d3MzP+Hlt2KXKryffhnmT4JONMCiY6DmDmCHj2uJRLEJnHF9aXTUvHviAUlU66BTMzx2I9/GTteHW8+7HdcQos2cBQgiyM0qNmZ2TCtHrjQEaDo62BEX4Ehrph4dX+2R27ohI02gh0jTanoorGpLP5pEUn0tJUe2Bqd793AmN8qP/wB7Y2Jq3DHHtAa/zQb3ZF6Wm2kZBtPPtLB41ta0eo13pbOOrrKqK1YfXU26XhXuxgbmxKuxzcoDGD3Zej4orGpJqQsHLStWm9oAgLwaGe9M30NPs8dSVkabRQqRptA82Ngrc3ZyJj83i7K/ZpCUWmHRzcLQlKNyX0Cjzvhlem0qiwsWJPSPsyPK1ozeR/Hn8PGzbuZRna9OZxtfFogL+dXI9BlUJ0fFqRiVWotDrm0wh0xhXZ64JsTlk1Jm5OrvaExLpS/hgP/oFeHUKvdoLaRotRJpG+9AgjYi6muSzeSTE5lCUX2G6zqdnt5rQ3RuvQasvXCBv8wZTAsT4AEd+HOqMHX14fvwjdHO0noI3zaWzjK8T6clsSd6G95UrTPqpAq/Lxn2uppJVXotpjyw+l8ry2j2yq7Uq/Pt7oFQqOo1e7Yk0jRYiTaN9aEovIQSFeeWci80h5VweWk1ttMuAUG9CIn3x6dmtyXXua9NjlzsoOTTClQwvH/444hH6enq1y/O1Np1hfH0Ze4wD2f9h9LkyhiZUogRTgkGn0LAm32dONJ6Tc/26Gp1Br/ZGmkYLkabRPpijV7VWT2pSAQmxOQ3i6q/W/HB0arwMrCY7m7zNG1HXFOJJ6mPP4age3BPZMQ8BduTxZTAYWHfsa0ozDzHp5BXcr+hBocB90hQ8axIMNkZhXjkJsTlmnfu5lo6sl6WQptFCpGm0D83Vq6SowlRCs+4J3v4DexAa1fgJXmMCxAMUfL4TtFqq7BQcHtKNnsNiiBnasSKrOur4qtSqeX3/JkLjY4k8b8xXZtezFz4PLa6XYPAqxgwDeSTE5l6TYcC1ZpnSu9EMA9fSUfWyJNI0Wog0jfahpXpdL1dQSKQvIY3kCqouLCB700Y0iQkApPe0I37YUJ64Y3Gj5UKtkY44vs7lZLJn9zrG/5aLa6UBg1JJj+kz8Zw+E4Vt7Qe/EIKcmlxmaY3mMvOlh0/zalV0RL0sjTSNFiJNo31oDb3Ky9TGmh+x9bOS+vc3ZiXtN7A2K6kQgstHj3Dp462otNVobBX8FOHFuLufILRn31Z7rraio42vHUd2Y//9V4ReNIbA6vz8CHz0cex71yYYrKzQkhSfS0JcDpdvMmvytXQ0vawBaRotRJpG+9Cael2tf5AYl0NaciGGq6G7TiqCI3wJjfLF3dMYuqsrLSXh/XewT04GIMvLjsuTZjD79rtu7oHamI4yvsqqKvnsozcZ+ut5nDQCnY2SbjNm0Wv6TBRKJQaDIDPdGCp7bX2WkJpaFd3dbz7KraPoZU1I02gh0jTah7bSq6pSawrdrVtpzbem0lpgsBcqOxuyjx4h/+PNOGl06GwgPrwfdy75M67O1nliuCOMr9hzceRsf4+AHGPIdKmfN5FP/AEHXz9jJci4XBLjc6i4YgyVVSigb6AnoYP96BNwc5Ugr6Uj6GVtSNNoIdI02oe21ksIQX7OlZpEdXmmms4qOxsGhnkTGuWHm7Pg+Lo38D1/AYB8NzuUs+5jzLiJrd6fm8Wax5dGq2HPlnUEnI7FvlqgsVUgpt1J2PS7uVCz/5R1obbmfHf3q6GyPji7tE7N+WuxZr2sFWkaLUSaRvvQnnppNTpSEwtIiMsh71KZqd3T25nQKD/URWdQfPMZ3Sp1GBSQHNSLMYv/SA9PzzbtV3Ow1vH184kfqfh8G35Fxr2LLD93+t33JNk5BpLP5KFRG0NlbWyVBAYbQ2X9/JsOlW0trFUva0aaRguRptE+WEqv4oIKEuJySD6Ti7pKZ+qLf4AbVakHCT0fi42AMicbSiZOYvL/zGu3vl0PaxtfZWWX+X7DGww8d8Gol6M9mUPvwKD0Jz+n9m+oh7exGNfAcG/sHdqvVoW16dURkKbRQqRptA+W1kuvM5B+vpDEuBwy02uXTuwdwK0oloH5idjrq0jv5U7wQ0/Sr3/DMwXtiaX1qsv3e77Eac83dC/XUebgRWLvKNS2feqEytowMMxY9tfLt3mhsq2FNenVUZCm0UKkabQP1qRX7SZtLhVXNDWtAo/KTHqXJuOqzeZi+ADGzH8UTwstWVmDXrG/niLvy4/omVNFrmsgme5BqG3dTK/79e5OSJQfgSFeqFoYKttaWINeHQ1pGi1Emkb7YI16NRUOaqerxK8sBXdNKkUR/Zg4fylO7RxlZUm9Us4nkvTpRtzzbclxHUiBSx+EwmgKjk6qmnoofrh7Xj/ZYHtijePL2pGm0UKkabQP1q5XZYWW5JoaDaV1Dp65V+bgrklBF+HDlPsWoVK1zzq9JfS6dCmTUx9txq7QmTzXgahVLsYXFNAnwIPQSD/6Dqg9QGlNWPv4skakabQQaRrtQ0fRSwhBbtZlzv2WzflzeQhhjPqx1Wtw01xA1deO2++Zg2s38woGtZT21Csp4Sy/fXsIUeZGiWMv44EKwMFRSWR0H4IbSdVibXSU8WVNtJVpyKK6ki6FQqHAz98NP383xk4OIulMDqcOn0WLA4VOwVAAX7yxD5VjMVF3jCFsUISlu9wi9Ho9B7/5LwVxuVQqe1NtEwFOoBB63L1sueX2QfTq2zAppERyI6RpSLos9g62REb7ExntT9aFAr7/+kcqrjhTYd8DDD048nUup7/6Fc8QdybNmoKdyvqTIebn53No517UxQ5UqrxAZfy2qDKU4R3gzOS7xjWZfl4iMQe5PNUEcjrcPDqLXhpNNQe++YG8pBLUyh6mdpW+EnubQjwCPbjtzttueuO8NfW6mJ7JiX0/oi6ASqU3Qmnc1FYatDjaFTN4YhSDhoR06FlFZxlf7UmXXp46d+4cf/vb30hJSaFv3768+OKLDB482NLdknRC7O1V3DnndgASzybz854TaKo80No6U00fylPhozd/xF6RT7fezoy5YyzeXt7t2kedTse5+ATO/hiL9rKKKhsvhMLP9NfsqCvAxRem3DuNbt0sc65C0nmx+pmGRqNh8uTJLFu2jHvuuYevvvqKN998k4MHD2JnRu0EOdNoHzqzXjqdjiP7j3ApPgOtxg2NbffaF4UBB30ZNsor2Lsp8Rvoz/Cxw3G8Qf3y5uiVfSmXX4/9TGlmMfpKW7QKN6ptasNhFcKAo74Ae7dqBk8cTkhY8E09rzXSmcdXW9FlZxrHjx9HqVQyf/58AGJiYti8eTOHDh1i6tSpFu6dpCtga2vLbdNug2nGf584coKUU0lUVzijtnWvORDnRkUZFJ82kHDqKHaGMpRoUNpUo7QHlZMKZw8XXN26obBRolQocHCwRa3WYRACnVbH5cIS1Jer0FXpMVQrEAY79Diise0GuBh/av5ibfQaHEQRjt5KRt0xDn9/60vKKOmcWL1ppKenExhYP+VD//79OX/+vFmmoVAoaEmGZqVSUe+/kuvTlfQaM2EUYyaMAqC09DInD58kPy2H6isKdKI7GltX1EqP2jdojT9FpQAC0Ne8oKtzVwVQ5z3Kmh+MEU8OulJsVBU4etrRf9AAho4ch62t1f/5thpdaXy1Fm2lmdWPusrKygZTfQcHB9RqtVnv9/R0vqkNQDc366zHYK10Nb08PFwICJhdr+18cjpnfzlLSW4xFaWV6Cr1GKqVGAx2GGjq8KBAiRalTTU29gI7ZztcPF3w8fdhxNhhuLl1b+J9XYuuNr5ag9bWzOpNw9HRsYFBqNVqnJzMS3FQVFTR4pmGm5szpaUVpvQTkqaRetXi2cOLW6dMuO41zdHLYIDi4vJW7GHHQ46v5nOzmnl4uDTabvWmERAQwLZt2+q1paenM2PGDLPeL4RAr7/xdU1hMAi58dYMpF7NQ+rVPKRezae1NbO+JDPXMHr0aLRaLVu3bqW6uprPPvuMwsJCxo4da+muSSQSSZfD6k3Dzs6O9evX8+233zJixAi2bdvGunXrzF6ekkgkEknrYfXLUwAhISF88sknlu6GRCKRdHmsfqYhkUgkEutBmoZEIpFIzEaahkQikUjMRpqGRCKRSMzG6hMWSiQSicR6kDMNiUQikZiNNA2JRCKRmI00DYlEIpGYjTQNiUQikZiNNA2JRCKRmI00DYlEIpGYjTQNiUQikZiNNA2JRCKRmI00I8irDgAADpVJREFUDYlEIpGYjTSNRnjnnXeYMGEC0dHRLFiwgOTkZNNrx44dY8aMGQwePJj58+eTnp5uwZ5aF6tWreIf//hHvTapV0POnTtHTEwMgwcPZtasWfz222+W7pLVEhcXV6/g2uXLl3niiScYNmwYEyZMYOfOnRbsnfXw888/c8899zBs2DAmTZpkKiXRJnoJST127dolpkyZIjIyMkR1dbV4++23xYQJE4RerxcFBQViyJAh4sCBA0Kj0Yi1a9eK2bNnW7rLFqe4uFg888wzIigoSPz97383tUu9GqJWq8W4cePERx99JLRardi5c6e45ZZbhEajsXTXrAqDwSB27twphg0bJkaMGGFqf+qpp8Sf/vQnoVarRWxsrBgxYoRISEiwYE8tT2lpqRg+fLj46quvhF6vF2fOnBHDhw8XR48ebRO95EzjGkpKSli2bBn+/v7Y2tqycOFCsrOzyc3NZd++fYSGhjJx4kTs7Ox47LHHyMzM5MyZM5butkWZP38+NjY2TJ06tV671Kshx48fR6lUMn/+fFQqFTExMbi7u3Po0CFLd82qePfdd9myZQvLli0ztVVUVLB//36WL1+Ovb09kZGRzJgxo8vPNrKzsxk/fjx33XUXSqWS8PBwRo4cyS+//NImenVJ09DpdJSVlTX4KS8vZ8mSJcyePdt07cGDB3Fzc8PX15e0tDQCAwNNr9nY2ODv709KSoolHqPduJ5eAJs2bWL16tUNSvB2Vb2uR3p6ej1NAPr378/58+ct1CPrZM6cOXz11VcMGjTI1Hbx4kVsbW3x9/c3tUntIDQ0lH/+85+mf1++fJmff/4ZoE306hDlXlubkydPsmjRogbtvXr14uDBg6Z/nzp1ipUrV/LSSy+hVCqpqqrCxcWl3nscHR2pqqpq8z5bkhvp5ePj0+j7uqpe16OyshJHR8d6bQ4ODqjVagv1yDrx9vZu0FZZWYmDg0O9Nqldfa5cucKyZctMs40tW7bUe7019OqSpjFmzBiSkpKue82XX37Jiy++yIoVK5g5cyZg/MC7VvCqqqoG37A7G+bo1RhdVa/r0ZgmarW6S2tiLlK765OZmWlaWn/zzTdJTU1tE7265PLUjXj77bd59dVXeeedd7j77rtN7QEBAfWif/R6PRkZGQwYMMAS3bR6pF4NuVYTMC5ZdWVNzKVv377odDqys7NNbVI7I2fPnuXee+9l7NixvPPOOzg4OLSZXtI0rmHXrl1s3ryZjz/+mNGjR9d7bfLkyZw5c4Z9+/ah1WpZt24dvr6+hIWFWai31o3UqyGjR49Gq9WydetWqqur+eyzzygsLKwXVippHBcXF26//XZef/11qqqqiIuL45tvvjGtBHRVCgsLefjhh1m0aBHPPfccSqXxY72t9JKV+65h6tSpZGVlYWdnV6/9s88+IzAwkOPHj/PKK6+QmZlJaGgoq1evpn///hbqrXXx7LPP4u7uzjPPPGNqk3o1JDExkRdeeIGkpCT69u3LCy+8wODBgy3dLavkxIkTLF++nBMnTgBQWlrKypUr+emnn3BycuLJJ58kJibGwr20LO+++y5vvPFGg2WnhQsXsmjRolbXS5qGRCKRSMxGLk9JJBKJxGykaUgkEonEbKRpSCQSicRspGlIJBKJxGykaUgkEonEbKRpSCQSicRspGlIrJ6srCz279/fZvdfu3ZtvZP/rcHEiRPZtm1bm13fFM15FiEEO3bsQKPRNPu9kq6LNA2J1fPcc89x+vRpS3ejQ7B48WI2bNhg1rWnTp1ixYoV6HS6Zr9X0nXpkgkLJZLOirOzM87OzmZde+253ua8V9J1kTMNiVWwfft2Jk2aREREBDNmzOC7774DjKlJTp48ycaNG1mwYAEAsbGxLFiwgMGDBxMZGcm8efNITEwEjEtZwcHBfPfdd0ybNo0hQ4bw4IMPcuHCBdPvio2NJSYmhsjISBYtWkRJSUm9vhw+fJg5c+YQGRnJkCFDWLJkiSnp2+eff86cOXP44x//yLBhw0zfzNevX8/YsWOJjo7m3XffveHz3uj6Xbt2MWXKFKKiopgzZw7Hjh0DjOVzw8PDKS0tNV2bm5tLSEgIiYmJDZaYvvjiC2bMmEFERATR0dH87ne/o6ysjKysLBYuXAjA0KFDOXHiRIP3XtV5yJAhjBs3jrVr12IwGABjeo9bbrmFzz//nIkTJxIdHc1jjz1GcXExYKzB8uKLLzJmzBiioqJYuHBhl6970Wm46VqDEslNcvbsWRESEiL27NkjsrKyxHvvvSfCw8NFYWGhKCsrE3PnzhUrV64UJSUl4sqVK2L48OHitddeExkZGSI+Pl7ce++9YsGCBUIIITIzM0VQUJCYMWOGOHXqlIiNjRVTp04Vjz/+uBBCiKKiIhEdHS1eeOEFkZqaKrZt2ybCwsJMZWgzMjJEeHi42Lx5s8jMzBSnTp0SU6ZMEc8++6wQwlgOOCgoSLz88ssiPT1d5OTkiB07doghQ4aI3bt3i+TkZPHoo4+KoKAgsXXr1kaf90bXf//992L48OFi9+7d4sKFC2Lz5s0iIiJCJCYmCr1eL2655Raxc+dO0/0+/PBDMX36dCGEEG+99ZbpWU6dOiXCw8PF119/LbKyssQPP/wgRo4cKdauXSt0Op3Yu3evCAoKEhkZGUKj0dR7b2pqqoiMjBSrVq0SKSkpYt++fWLEiBFi3bp1Qgghjh8/LsLCwsR9990nzpw5I3766ScxatQosXr1alOfxo8fL3777Tdx8eJF8dRTT4lZs2a13qCRWAy5PCWxOJcuXUKhUNCrVy969erFI488QlhYGI6Ojjg5OaFSqXB0dMTNzY2CggKWLl3K4sWLUSqV+Pv7M3v2bN56661693zssceIjo4GjOVo169fD8Du3btxcHDg+eefx9bWloCAAE6ePElmZiZgTN/+3HPPcf/99wPQu3dvpkyZwvHjx+vd//HHH8fDwwOATz75hHnz5jFt2jQAXn31VcaPH9/k897o+vfff58lS5aYXl+4cCGxsbFs2bKF1atXc8cdd7B3715T4rndu3czY8aMBr/HwcGBVatWmV7r1asXY8aMISUlBRsbG7p37w6Ah4dHgwSdO3bsoE+fPjz//PMABAYGUlBQwOuvv86jjz4KGGcTzz77LOHh4QDcddddxMbGAsYZn4ODA71798bT05OVK1eSlpbWpCaSjoM0DYnFGTt2LMOHD2fOnDkMGDCA2267jZiYmEaLxXh5eRETE8OWLVtISkoiPT2ds2fPNri2b9++pv93cXGhuroagJSUFIKCgrC1rR36gwYNMplGv379cHR05P333yc5OZm0tDSSkpIIDg42Xe/k5GQyDIDU1NR6lQ3d3d3rldi8lhtdn5KSQlxcXL1lq+rqaiIjIwGYOXMm8+fPp6ysjIqKCuLi4njttdca/J6IiAicnJxYu3YtqamppKamkpKSwuTJk5vsW90+REVF1WsbOnQo5eXl5OXlmdqa0vmBBx5g//79jBs3jiFDhnD77bczZ86cG/5eifUjTUNicRwdHdm0aROnT5/m+++/58CBA3z00Uds2rSpwQdXfn4+d999N0FBQYwbN45Zs2aRmpraYKahUqnq/VvU2fQV12wA1zWQ5ORk5s6dy7hx4xgxYgTz58/n0KFDHD161HTNtd/KFQrFde95LTe6Xq/X8/TTT3PbbbfVu+bq742MjKRnz54cPHiQkpISoqKiGjWpY8eOsXTpUmbOnMmoUaN45JFH2Lhxo+mD/XrY29ujUCjqtV3dz7j6X2ha5379+rF3716OHDnC4cOH+eCDD9i+fTuff/45rq6uN/z9EutFmobE4vzyyy/8+OOPLF++nOjoaJ5++mmmT5/OoUOHGpjGd999h52dHRs2bDB9qP3www9m/67g4GD27t2LVqs1fQifPXvW9PoXX3xBeHh4PRPavHnzde8ZFBREbGysqbhNeXk5GRkZLb4+MDCQS5cu1fsW/69//YsePXqYNq+nT5/OgQMHKCwsbHRpCozLYNOnT+fVV181tV28eBE/Pz+ABqZQl8DAQA4dOlSv7ddff8XFxQUvLy/TzKwpvvjiC5RKJbNmzWLSpEksX76csWPHcubMmQbFzSQdCxk9JbE4Tk5OvPfee2zdupWsrCwOHTrEpUuXiIiIAIyhoBkZGRQWFuLm5kZhYSE//PADWVlZbN++nW3btqHVas36XdOnT0epVLJixQpSU1PZuXMne/bsMb3u7u5OWloap0+fJiMjg3Xr1plMpikefPBBduzYwZdffklqairPP/98g9rMzbn+4Ycf5pNPPuHTTz8lIyODTZs2sX79evr162e6ZubMmRw5coT4+HjuuOOORn+Pm5sbcXFxnDt3jrS0NFatWkV8fLzpWa4u6SUkJJgO+F3l/vvvJysri9WrV5OWlsZ3333HW2+9xfz58xvMLhqjsrKSV155hcOHD5OVlcWuXbuwt7eXpVk7AXKmIbE4ISEhrFmzhrfffps1a9bg5eXF73//eyZNmgTA3LlzeeaZZ1i8eDFffvklv/zyC3/5y1/Q6/UEBQXx4osv8uyzz3LhwoXrLgsBuLq6snHjRlauXMns2bMJDQ3lgQceMFWGW7BgAYmJiSxduhRbW1siIiL461//ymuvvUZ5eXmj97zzzjspLS3ljTfeoKysjHvvvZfQ0NAm+3Cj6ydPnsz//u//smHDBl5++WX8/f1Zs2YNt956q+magIAAAgICcHd3x9PTs9Hfs3z5ctOmvqOjI9HR0Tz11FPs3LkTIQRBQUGMHTuWhx56iH/+85/13uvj48P777/PmjVr2L59O15eXixatIilS5deV9+rzJs3j/z8fFasWEFxcTEDBgzgnXfewcvLy6z3S6wXWblPIpFIJGYjl6ckEolEYjbSNCQSiURiNtI0JBKJRGI20jQkEolEYjbSNCQSiURiNtI0JBKJRGI20jQkEolEYjbSNCQSiURiNv8PZxamR/XTQBYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d757358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(-20, 20)\n",
    "\n",
    "def huber_loss(t, c=3):\n",
    "    return ((abs(t) < c) * 0.5 * t ** 2\n",
    "            + (abs(t) >= c) * -c * (0.5 * c - abs(t)))\n",
    "\n",
    "plt.plot(t, 0.5 * t ** 2, label=\"squared loss\", lw=2)\n",
    "for c in (10, 5, 3):\n",
    "    plt.plot(t, huber_loss(t, c), label=\"Huber loss, c={0}\".format(c), lw=2)\n",
    "plt.ylabel('loss')\n",
    "plt.xlabel('standard deviations')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The Huber loss is equivalent to the squared loss for points which are well-fit by the model, but reduces the loss contribution of outliers. For example, a point 20 standard deviations from the fit has a squared loss of 200, but a c=3 Huber loss of just over 55. Let's see the result of the best-fit line using the Huber loss rather than the squared loss. We'll plot the squared loss result in light gray for comparison:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x135bfa400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def total_huber_loss(theta, x=x, y=y, e=e, c=3):\n",
    "    return huber_loss((y - theta[0] - theta[1] * x) / e, c).sum()\n",
    "\n",
    "theta2 = optimize.fmin(total_huber_loss, [0, 0], disp=False)\n",
    "\n",
    "plt.errorbar(x, y, e, fmt='.k', ecolor='gray')\n",
    "plt.plot(xfit, theta1[0] + theta1[1] * xfit, color='lightgray')\n",
    "plt.plot(xfit, theta2[0] + theta2[1] * xfit, color='black')\n",
    "plt.title('Maximum Likelihood fit: Huber loss');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "By eye, this seems to have worked as desired: the fit is much closer to our intuition!\n",
    "\n",
    "However a Bayesian might point out that the motivation for this new loss function is a bit suspect: as we showed, the squared-loss can be straightforwardly derived from a Gaussian likelihood. The Huber loss seems a bit *ad hoc*: where does it come from? How should we decide what value of $c$ to use? Is there any good motivation for using a linear loss on outliers, or should we simply remove them instead? How might this choice affect our resulting model?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### A Bayesian Approach to Outliers: Nuisance Parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Bayesian approach to accounting for outliers generally involves *modifying the model* so that the outliers are accounted for. For this data, it is abundantly clear that a simple straight line is not a good fit to our data. So let's propose a more complicated model that has the flexibility to account for outliers. One option is to choose a mixture between a signal and a background:\n",
    "\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "p(\\{x_i\\}, \\{y_i\\},\\{e_i\\}~|~\\theta,\\{g_i\\},\\sigma,\\sigma_b) = & \\frac{g_i}{\\sqrt{2\\pi e_i^2}}\\exp\\left[\\frac{-\\left(\\hat{y}(x_i~|~\\theta) - y_i\\right)^2}{2e_i^2}\\right] \\\\\n",
    "&+ \\frac{1 - g_i}{\\sqrt{2\\pi \\sigma_B^2}}\\exp\\left[\\frac{-\\left(\\hat{y}(x_i~|~\\theta) - y_i\\right)^2}{2\\sigma_B^2}\\right]\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "What we've done is expanded our model with some nuisance parameters: $\\{g_i\\}$ is a series of weights which range from 0 to 1 and encode for each point $i$ the degree to which it fits the model. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "$g_i=0$ indicates an outlier, in which case a Gaussian of width $\\sigma_B$ is used in the computation of the likelihood. This $\\sigma_B$ can also be a nuisance parameter, or its value can be set at a sufficiently high number, say 50."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Our model is much more complicated now: it has 22 parameters rather than 2, but the majority of these can be considered nuisance parameters, which can be marginalized-out in the end, just as we marginalized (integrated) over $p$ in the Billiard example.  Let's construct a function which implements this likelihood. We'll use the [emcee](http://dan.iel.fm/emcee/current/) package to explore the parameter space."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "To actually compute this, we'll start by defining functions describing our prior, our likelihood function, and our posterior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# theta will be an array of length 2 + N, where N is the number of points\n",
    "# theta[0] is the intercept, theta[1] is the slope,\n",
    "# and theta[2 + i] is the weight g_i\n",
    "\n",
    "def log_prior(theta):\n",
    "    #g_i needs to be between 0 and 1\n",
    "    if (all(theta[2:] > 0) and all(theta[2:] < 1)):\n",
    "        return 0\n",
    "    else:\n",
    "        return -np.inf  # recall log(0) = -inf\n",
    "\n",
    "def log_likelihood(theta, x, y, e, sigma_B):\n",
    "    dy = y - theta[0] - theta[1] * x\n",
    "    g = np.clip(theta[2:], 0, 1)  # g<0 or g>1 leads to NaNs in logarithm\n",
    "    logL1 = np.log(g) - 0.5 * np.log(2 * np.pi * e ** 2) - 0.5 * (dy / e) ** 2\n",
    "    logL2 = np.log(1 - g) - 0.5 * np.log(2 * np.pi * sigma_B ** 2) - 0.5 * (dy / sigma_B) ** 2\n",
    "    return np.sum(np.logaddexp(logL1, logL2))\n",
    "\n",
    "def log_posterior(theta, x, y, e, sigma_B):\n",
    "    return log_prior(theta) + log_likelihood(theta, x, y, e, sigma_B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now we'll run the MCMC samples to explore the parameter space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /Applications/anaconda3/envs/SNF-env/lib/python3.5/site-packages/ipykernel_launcher.py:16: RuntimeWarning:divide by zero encountered in log\n",
      " /Applications/anaconda3/envs/SNF-env/lib/python3.5/site-packages/ipykernel_launcher.py:15: RuntimeWarning:divide by zero encountered in log\n"
     ]
    }
   ],
   "source": [
    "# Note that this step will take a few minutes to run!\n",
    "\n",
    "ndim = 2 + len(x)  # number of parameters in the model\n",
    "nwalkers = 50  # number of MCMC walkers\n",
    "nburn = 10000  # \"burn-in\" period to let chains stabilize\n",
    "nsteps = 15000  # number of MCMC steps to take\n",
    "\n",
    "# set theta near the maximum likelihood, with \n",
    "np.random.seed(0)\n",
    "starting_guesses = np.zeros((nwalkers, ndim))\n",
    "starting_guesses[:, :2] = np.random.normal(theta1, 1, (nwalkers, 2))\n",
    "starting_guesses[:, 2:] = np.random.normal(0.5, 0.1, (nwalkers, ndim - 2))\n",
    "\n",
    "import emcee\n",
    "sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[x, y, e, 50])\n",
    "sampler.run_mcmc(starting_guesses, nsteps)\n",
    "\n",
    "sample = sampler.chain  # shape = (nwalkers, nsteps, ndim)\n",
    "sample = sampler.chain[:, nburn:, :].reshape(-1, ndim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Once we have these samples, we can exploit a very nice property of the Markov chains. Because their distribution models the posterior, we can integrate out (i.e. marginalize) over nuisance parameters simply by ignoring them!\n",
    "\n",
    "We can look at the (marginalized) distribution of slopes and intercepts by examining the first two columns of the sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120c66f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sample[:, 0], sample[:, 1], ',k', alpha=0.1)\n",
    "plt.xlabel('intercept')\n",
    "plt.ylabel('slope');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We see a distribution of points near a slope of $\\sim 0.4-0.5$, and an intercept of $\\sim 29-34$. We'll plot this model over the data below, but first let's see what other information we can extract from this trace.\n",
    "\n",
    "One nice feature of analyzing MCMC samples is that the choice of nuisance parameters is completely symmetric: just as we can treat the $\\{g_i\\}$ as nuisance parameters, we can also treat the slope and intercept as nuisance parameters! Let's do this, and check the posterior for $g_1$ and $g_2$, the outlier flag for the first two points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g1 mean: 0.59\n",
      "g2 mean: 0.36\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x136638ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sample[:, 2], sample[:, 3], ',k', alpha=0.1)\n",
    "plt.xlabel('$g_1$')\n",
    "plt.ylabel('$g_2$')\n",
    "\n",
    "print(\"g1 mean: {0:.2f}\".format(sample[:, 2].mean()))\n",
    "print(\"g2 mean: {0:.2f}\".format(sample[:, 3].mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "There is not an extremely strong constraint on either of these, but we do see that $(g_1, g_2) = (1, 0)$ is slightly favored: the means of $g_1$ and $g_2$ are greater than and less than 0.5, respecively. If we choose a cutoff at $g=0.5$, our algorithm has identified $g_2$ as an outlier.\n",
    "\n",
    "Let's make use of all this information, and plot the marginalized best model over the original data. As a bonus, we'll draw red circles to indicate which points the model detects as outliers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "theta3 = np.mean(sample[:, :2], 0)\n",
    "g = np.mean(sample[:, 2:], 0)\n",
    "outliers = (g < 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x133749ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(x, y, e, fmt='.k', ecolor='gray')\n",
    "plt.plot(xfit, theta1[0] + theta1[1] * xfit, color='lightgray')\n",
    "plt.plot(xfit, theta2[0] + theta2[1] * xfit, color='lightgray')\n",
    "plt.plot(xfit, theta3[0] + theta3[1] * xfit, color='black')\n",
    "plt.scatter(x[outliers], y[outliers],marker='o',s=40,edgecolors='r',linewidths=2,c='k')\n",
    "plt.title('Maximum Likelihood fit: Bayesian Marginalization');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result, shown by the dark line, matches our intuition! Furthermore, the points automatically identified as outliers are the ones we would identify by hand.  For comparison, the gray lines show the two previous approaches: the simple maximum likelihood and the frequentist approach based on Huber loss."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Discussion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Here we've dived into linear regression in the presence of outliers. A typical Gaussian maximum likelihood approach fails to account for the outliers, but we were able to correct this in the frequentist paradigm by modifying the loss function, and in the Bayesian paradigm by adopting a mixture model with a large number of nuisance parameters.\n",
    "\n",
    "Both approaches have their advantages and disadvantages: the frequentist approach here is relatively straightforward and computationally efficient, but is based on the use of a loss function which is not particularly well-motivated. The Bayesian approach is well-founded and produces very nice results, but requires a rather subjective specification of a prior. It is also much more intensive in both coding time and computational time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "For Bayes' billiard ball example, we showed that a naïve frequentist approach leads to the wrong answer, while a naïve Bayesian approach leads to the correct answer. This doesn't mean frequentism is wrong, but it does mean we must be very careful when applying it.\n",
    "\n",
    "For the linear regression example, we showed one possible approach from both frequentism and Bayesianism for accounting for outliers in our data. Using a robust frequentist cost function is relatively fast and painless, but is dubiously motivated and leads to results which are difficult to interpret. Using a Bayesian mixture model takes more effort and requires more intensive computation, but leads to a very nice result in which multiple questions can be answered at once: in this case, marginalizing one way to find the best-fit model, and marginalizing another way to identify outliers in the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Maskininlärning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Utrusta datorer med kapaciteten att \"lära sig\" från \"data\".\n",
    "    * Data från t.ex. sensorer, internet, ...\n",
    "    * ... eller från experiment, teoretiska simuleringar\n",
    "    * Förväntning att datorn skall göra \"rimliga\" förutsägelser."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Kategoriseras som\n",
    "    * Supervised learning (klassifisering, regression)\n",
    "    * Unsupervised learning (dimensionalitetsreduktion, clustering)\n",
    "    * Reinforcement learning (inlärning med försenad återkoppling)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![](figures/machine_learning.png)\n",
    "XKCD web comic: [Machine learning](https://xkcd.com/1838/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Maskininlärning del 1:\n",
    "### Neurala nätverk, deep learning och TensorFlow\n",
    "\n",
    "![](figures/400px-neural_network.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Tillämpningar inom allt möjligt\n",
    "* Textigenkänning\n",
    "* Bildigenkänning\n",
    "* Taligenkänning\n",
    "* Översättning\n",
    "* Medicinsk diagnos\n",
    "* Självkörande bilar\n",
    "* mm, mm,mm\n",
    "\n",
    "Mycket av detta har blivit möjligt genom tillgång till \n",
    "* stora datamängder (att träna på) \n",
    "* nya algoritmer (t.ex. deep learning) \n",
    "* samt ny teknologi (t.ex. gpu) som möjliggör att utföra maskininlärningen i praktiken."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Exempel: Bildigenkänning med områdesbeskrivningar\n",
    "![](figures/deep_learning_image_descriptions.png)\n",
    "från [arXiv:1412.2306](https://arxiv.org/abs/1412.2306)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Exempel: Addition av två tal som strängar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "För den vill vill testa att bygga ett neuralt nätverk rekommenderas [TensorFlow](https://www.tensorflow.org/) som är ett öppet programbibliotek för maskinintelligens genom neurala nätverk. Personligen tyckte jag att TensorFlow blir enklare att använda genom ett python API som heter [Keras](https://keras.io/).\n",
    "\n",
    "Ett exempel från deras [exempelbibliotek](https://github.com/keras-team/keras/tree/master/examples) finns i en separat [ipython notebook](Keras_Addition_rnn.ipynb) som ni gärna får testa.\n",
    "\n",
    "Uppgiften är att lära ett neuralt nätverk med tre lager och 200.000 parametrar att addera två tresiffriga tal. Både själva additionen och svaret skall representeras som strängar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Extracted output from Keras_Addition_rnn.ipynb\n",
    "\n",
    "# model.system()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "```\n",
    "_________________________________________________________________\n",
    "Layer (type)                 Output Shape              Param #   \n",
    "=================================================================\n",
    "lstm_1 (LSTM)                (None, 128)               72192     \n",
    "_________________________________________________________________\n",
    "repeat_vector_1 (RepeatVecto (None, 4, 128)            0         \n",
    "_________________________________________________________________\n",
    "lstm_2 (LSTM)                (None, 4, 128)            131584    \n",
    "_________________________________________________________________\n",
    "time_distributed_1 (TimeDist (None, 4, 12)             1548      \n",
    "_________________________________________________________________\n",
    "activation_1 (Activation)    (None, 4, 12)             0         \n",
    "=================================================================\n",
    "Total params: 205,324\n",
    "Trainable params: 205,324\n",
    "Non-trainable params: 0\n",
    "_________________________________________________________________\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "```\n",
    "--------------------------------------------------\n",
    "Iteration 1\n",
    "Train on 45000 samples, validate on 5000 samples\n",
    "Epoch 1/1\n",
    "45000/45000 [==============================] - 26s 572us/step - loss: 1.8809 - acc: 0.3228 - val_loss: 1.7916 - val_acc: 0.3457\n",
    "Q 3+368   T 371  ☒ 13  \n",
    "Q 94+32   T 126  ☒ 101 \n",
    "Q 8+466   T 474  ☒ 102 \n",
    "Q 989+717 T 1706 ☒ 1100\n",
    "Q 4+125   T 129  ☒ 23  \n",
    "Q 996+41  T 1037 ☒ 100 \n",
    "Q 10+245  T 255  ☒ 132 \n",
    "Q 1+759   T 760  ☒ 122 \n",
    "Q 714+489 T 1203 ☒ 1107\n",
    "Q 517+649 T 1166 ☒ 1167\n",
    "\n",
    "--------------------------------------------------\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "[...]\n",
    "```\n",
    "--------------------------------------------------\n",
    "Iteration 15\n",
    "Train on 45000 samples, validate on 5000 samples\n",
    "Epoch 1/1\n",
    "45000/45000 [==============================] - 26s 572us/step - loss: 0.5331 - acc: 0.8062 - val_loss: 0.4613 - val_acc: 0.8338\n",
    "Q 491+493 T 984  ☒ 975 \n",
    "Q 459+48  T 507  ☒ 506 \n",
    "Q 910+974 T 1884 ☑ 1884\n",
    "Q 582+346 T 928  ☒ 927 \n",
    "Q 313+31  T 344  ☒ 334 \n",
    "Q 717+7   T 724  ☑ 724 \n",
    "Q 87+509  T 596  ☑ 596 \n",
    "Q 545+7   T 552  ☑ 552 \n",
    "Q 313+9   T 322  ☑ 322 \n",
    "Q 602+784 T 1386 ☒ 1387\n",
    "\n",
    "--------------------------------------------------\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "[...]\n",
    "```\n",
    "--------------------------------------------------\n",
    "Iteration 200\n",
    "Train on 45000 samples, validate on 5000 samples\n",
    "Epoch 1/1\n",
    "45000/45000 [==============================] - 16s 348us/step - loss: 0.0012 - acc: 1.0000 - val_loss: 0.0027 - val_acc: 0.9996\n",
    "Q 111+289 T 400  ☑ 400 \n",
    "Q 4+663   T 667  ☑ 667 \n",
    "Q 331+54  T 385  ☑ 385 \n",
    "Q 10+201  T 211  ☑ 211 \n",
    "Q 777+324 T 1101 ☑ 1101\n",
    "Q 9+693   T 702  ☑ 702 \n",
    "Q 470+75  T 545  ☑ 545 \n",
    "Q 999+571 T 1570 ☑ 1570\n",
    "Q 72+883  T 955  ☑ 955 \n",
    "Q 13+983  T 996  ☑ 996 \n",
    "\n",
    "--------------------------------------------------\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Fysiker är ofta väldigt snabba på att ta till sig nya möjligheter, och att utveckla dem vidare. Ofta erbjuder forskning inom fundamental fysik väldigt stora utmaningar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "![](figures/QMBwithANN_science.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Neutron Reconstruction using Neural Networks\n",
    "#### Master’s thesis in Subatomic Physics<br/>Marcus Polleryd, 2017 [pdf](http://publications.lib.chalmers.se/records/fulltext/253132/253132.pdf)\n",
    "![](figures/500px-NeuLANDevents.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Simulated output from the scintillator-based detector NeuLAND converted into 3-D images showing the deposited energy of particles traversing the detector, for both 1 and 5 incoming neutrons travelling in the positive z-direction. The axes, given in pixel number, represent the full geometry of NeuLAND."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Maskininlärning del 2:\n",
    "###  Gaussprocesser\n",
    "\n",
    "Antag att det finns en okänd funktion\n",
    "$$\n",
    "f: x \\mapsto y\n",
    "$$\n",
    "\n",
    "Betrakta sedan följande två frågeställningar: Givet $N$ datapunkter: input=$(x_0, x_1, \\ldots, x_N)$, output=$(y_0, y_1, \\ldots, y_N)$, vad blir din förutsägelse för:\n",
    "* $y=f(x)$, dvs hur tror vi att den obekanta funktionen ser ut?\n",
    "* min($(f(x)$) i något intervall, dvs vad är funktionens minimum (och var inträffar det?)\n",
    "\n",
    "Bägge dessa frågeställningar dyker ofta upp i väldigt olika sammanhang och tillämpningar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* En (flerdimensionell) *Gaussdistribution* beskrivs av en vektor med medelvärden $m$ samt en kovariansmatris $K$\n",
    "$$\n",
    "\\vec{f} = (f_1, \\ldots, f_n) \\sim \\mathcal{N}(m,K)\n",
    "$$\n",
    "* En *Gaussprocess* kan ses som en generalisering av ovanstående till oändligt många variabler. Gaussprocessen beskrivs av en funktion med medelvärden $m(x)$ samt en kovariansfunktion $K(x,x')$\n",
    "$$\n",
    "f(x) \\sim \\mathcal{GP}(m(x),K(x,x')),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "En Gaussprocess kan betraktas som en apriorifördelning till en okänd funktion $f(x)$ där vi inte behöver begränsa oss till en given uppsättning med basfunktioner. Vi skriver att\n",
    "$$\n",
    "f \\sim \\mathcal{GP}(m,K),\n",
    "$$\n",
    "där $m$ och $K$ representerar medel (mean) och kovarians. Innebörden blir att $f$ blir en stokastisk process vars värden för $n$ punkter $x_1, \\ldots, x_n$ dras från en $n$-dimensionell normalfördelning\n",
    "$$\n",
    "f(x_1), \\ldots, f(x_n) \\sim \\mathcal{N}\\left( \\left( m(x_1,\\ldots,m(x_n) \\right), K(x_1,\\ldots,x_n) \\right).\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#------------------------------------------------------------\n",
    "# define a squared exponential covariance function\n",
    "# also known as the RBF kernel\n",
    "def squared_exponential(x1, x2, h):\n",
    "    return np.exp(-0.5 * (x1 - x2) ** 2 / h ** 2)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# draw samples from the unconstrained covariance\n",
    "np.random.seed(1)\n",
    "xtest = np.linspace(-3, 3, 100)\n",
    "h = 1.0\n",
    "\n",
    "mu = np.zeros(len(xtest))\n",
    "C = squared_exponential(xtest, xtest[:, None], h)\n",
    "draws = np.random.multivariate_normal(mu, C, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x134bbda20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#------------------------------------------------------------\n",
    "# Plot the diagrams\n",
    "fig = plt.figure(figsize=(5, 5))\n",
    "\n",
    "\n",
    "# first: plot a selection of unconstrained functions\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(xtest, draws.T, '-k')\n",
    "ax.set_ylabel('$f(x)$');\n",
    "ax.set_xlabel('$x$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Exempel #1: <br/>1-dim regression\n",
    "\n",
    "Vi kommer att demonstrera grundläggande principer för Gaussprocesser samt visa ett exempel på konstruktion av en endimensionell modell för regression.\n",
    "\n",
    "Det blir kortfattat. Ett bra litteraturtips för mer detaljer är boken [Gaussian Processes for Machine Learning](http://gaussianprocess.org/gpml/chapters/) av Carl Edward Rasmussen och Christopher K. I. Williams."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "För detta exempel generar vi först en uppsättning data $x,y$\n",
    "* $x$ representerar 'input' och $y$ representerar 'output'.\n",
    "* Eller $y = f(x)$ där funktionen $f(x)$ representerar en process som är okänd för oss. \n",
    "    * Det kan vara experimentell data som en funktion av en experimentellt modifierbar variabel;\n",
    "    * eller resultat från en teoretisk simulering som en funktion av en modellparameter.\n",
    "Vi kommer att låta observationerna $y$ inkludera slumpmässigt brus ('noise')."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "x = np.random.uniform(-3.,3.,(20,1))\n",
    "y = np.sin(x) + np.random.randn(20,1)*0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x135d044e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#------------------------------------------------------------\n",
    "# Plot the data sequentially as it is drawn. When can you guess the generating \"function\"\n",
    "fig, axarr = plt.subplots(3,2, sharex=True,sharey=True)\n",
    "\n",
    "for i,ni in enumerate([1,2,3,4,8,16]):\n",
    "    # Note the use of floor division '//' and modulo '%' to get the row and column\n",
    "    ax = axarr[i//2,i%2]\n",
    "    ax.plot(x[:ni], y[:ni], 'ok')\n",
    "    ax.text(0.1,0.8,'N=%i' %ni,transform=ax.transAxes)\n",
    "    if i%2==0: ax.set_ylabel('$f(x)$')\n",
    "    if i//2==2: ax.set_xlabel('$x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Gaussprocesser"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Först importerar vi modulen GPy. Det finns andra alternativ, t.e.x scikit-learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "import GPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "För att konstruera en GP modell behöver vi data och en kernel. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Vi definierar en RBF kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "kernel = GPy.kern.RBF(input_dim=1, variance=1., lengthscale=1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## GP modell utan optimering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "m = GPy.models.GPRegression(x,y,kernel)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Modellen konstrueras per default med lite brus (detta kan man givetvis ändra på). Vi använder funktionen 'display' för att se detaljer om modellen som vi har konstruerat innan vi ritar upp den."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: GP regression<br>\n",
       "<b>Objective</b>: 23.00549336414689<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 3<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-center{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:center;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  GP_regression.         </b></th><th><b>value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  rbf.variance           </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  rbf.lengthscale        </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  Gaussian_noise.variance</td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x134bb3748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x134c0ce48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import display\n",
    "display(m)\n",
    "fig = m.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Inte särskilt imponerande. Det skuggade bandet motsvarar 95% konfidensintervall (dvs +/- 2 standardavvikelser)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## Optimerad GP modell"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Nu är det dags att optimera GP modellen. Vi konstruerar modellen igen men försöker hitta de modellparametrar (varians, längdskala) som maximerar sannolikheten likelihood) att observera just denna data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running L-BFGS-B (Scipy implementation) Code:\n",
      "  runtime   i      f              |g|        \n",
      "    00s02  0006  -1.587157e+01   1.094179e+02 \n",
      "    00s05  0017  -1.958829e+01   8.597359e-04 \n",
      "    00s09  0026  -1.961517e+01   1.111500e-04 \n",
      "    00s10  0029  -1.961518e+01   7.375215e-12 \n",
      "    00s11  0030  -1.961518e+01   7.375215e-12 \n",
      "Runtime:     00s11\n",
      "Optimization status: Converged\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<paramz.optimization.optimization.opt_lbfgsb at 0x135bf24a8>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kernel = GPy.kern.RBF(input_dim=1, variance=1., lengthscale=1.)\n",
    "m = GPy.models.GPRegression(x,y,kernel)\n",
    "m.optimize(messages=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: GP regression<br>\n",
       "<b>Objective</b>: -19.615182381303452<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 3<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-center{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:center;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  GP_regression.         </b></th><th><b>               value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  rbf.variance           </td><td class=tg-right>  3.6636864469690558</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  rbf.lengthscale        </td><td class=tg-right>  2.3816491769068544</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  Gaussian_noise.variance</td><td class=tg-right>0.001130486250890581</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x135c6b128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1343c3438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(m)\n",
    "fig = m.plot(plot_density=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Vi använder datan som vi genererade ovan (och studerar hur vår modell blir bättre i takt med att vi lägger till mer data) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running L-BFGS-B (Scipy implementation) Code:\n",
      "  runtime   i      f              |g|        \n",
      "    00s01  0005   3.770669e+00   1.730130e+01 \n",
      "    00s03  0013   9.864801e-01   3.896196e-07 \n",
      "    00s04  0016   9.864333e-01   3.277358e-08 \n",
      "    00s06  0024   9.864297e-01   2.714134e-11 \n",
      "    00s06  0025   9.864297e-01   2.714134e-11 \n",
      "Runtime:     00s06\n",
      "Optimization status: Converged\n",
      "\n",
      "Running L-BFGS-B (Scipy implementation) Code:\n",
      "  runtime   i      f              |g|        \n",
      "    00s01  0005   4.277688e+00   2.981307e+00 \n",
      "    00s04  0013   3.307212e+00   4.635529e-03 \n",
      "    00s06  0019   3.290049e+00   2.737357e-07 \n",
      "    00s08  0025   3.289716e+00   1.865869e-06 \n",
      "    00s09  0029   3.289708e+00   4.945401e-09 \n",
      "    00s10  0032   3.289708e+00   7.067447e-11 \n",
      "Runtime:     00s10\n",
      "Optimization status: Converged\n",
      "\n",
      "Running L-BFGS-B (Scipy implementation) Code:\n",
      "  runtime   i      f              |g|        \n",
      "    00s01  0004   2.260508e+00   2.224909e+01 \n",
      "    00s01  0006   4.531032e+02   5.515472e+05 \n",
      "    00s04  0016  -1.419214e+00   7.440537e-09 \n",
      "    00s04  0018  -1.419214e+00   2.527427e-11 \n",
      "Runtime:     00s04\n",
      "Optimization status: Converged\n",
      "\n",
      "Running L-BFGS-B (Scipy implementation) Code:\n",
      "  runtime   i      f              |g|        \n",
      "    00s00  0004   1.097137e+05   5.238816e+09 \n",
      "    00s01  0005   1.022427e+01   2.076379e+03 \n",
      "    00s04  0014  -1.421268e+01   9.420381e-01 \n",
      "    00s06  0023  -1.481915e+01   2.803121e-01 \n",
      "    00s08  0029  -1.484951e+01   5.708999e-12 \n",
      "    00s08  0030  -1.484951e+01   5.708999e-12 \n",
      "Runtime:     00s08\n",
      "Optimization status: Converged\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d62fd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = GPy.plotting.plotting_library().figure(2, 2)\n",
    "\n",
    "for i,ni in enumerate([2,4,8,16]):\n",
    "    # Create model from data and kernel\n",
    "    kernel = GPy.kern.RBF(input_dim=1, variance=1., lengthscale=1.)\n",
    "    m = GPy.models.GPRegression(x[:ni], y[:ni],kernel)\n",
    "    # Optimize the model parameters to maximize the data likelihood\n",
    "    m.optimize(messages=True)\n",
    "    # Plot. Shaded bands indicate 95% confidence interval.\n",
    "    m.plot(figure=fig, row=(i//2+1), col=(i%2+1),legend=False)\n",
    "    ax =plt.gca()\n",
    "    ax.set_xlim([-3,3]); ax.set_ylim([-1.5,1.5])\n",
    "    ax.text(0.1,0.8,'N=%i' %ni,transform=ax.transAxes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Minns ni de stora parameterrummen i chiral EFT,\n",
    "\n",
    "... och den stora beräkningskostnaden för att göra en prediktion?\n",
    "\n",
    "Tänk er då att försöka göra en osäkerhetsanalys på en sådan teori."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Chiral effective field theory with machine learning\n",
    "#### Bachelor’s thesis in Subatomic Physics<br/>Johannes Aspman, Emil Ejbyfeldt, Anton Kollmats, Maximilian Leyman, 2016 [pdf](publications.lib.chalmers.se/records/fulltext/241791/241791.pdf)\n",
    "![](figures/boundstate_predict100000.png)\n",
    "11 parametrar, 100 träningspunkter, 100.000 emuleringar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Joint probability distribution of the radius of the deuteron, Rpt−p(2H), and the binding energy of the alpha particle, E(4He) for NLO. The black line is from 12,000 calculations with nsopt, dashed red lines are from 100,000 points predicted using 100 training points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Slutsats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Här framträder en bild av en modern ingenjör. Vi har gjort:\n",
    "* lite fysik, lite statistik, lite beräkningsfysik och lite maskininlärning;\n",
    "* tillsammans ger detta verktyg att ta oss an en väldigt bred palett av utmaningar;\n",
    "* och att försöka förstå vad våra resultat innebär."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Vem kan klara något sådant?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Svar: en fysiker"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Data science"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[The Data Science Venn Diagram](http://drewconway.com/zia/2013/3/26/the-data-science-venn-diagram) by Drew Conway."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](figures/Data_Science_VD.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "How to read the Data Science Venn Diagram\n",
    "\n",
    "The primary colors of data: hacking skills, math and stats knowledge, and substantive expertise\n",
    "\n",
    "* On Monday we spent a lot of time talking about \"where\" a course on data science might exist at a university. The conversation was largely rhetorical, as everyone was well aware of the inherent interdisciplinary nature of the these skills; but then, why have I highlighted these three? First, none is discipline specific, but more importantly, each of these skills are on their own very valuable, but when combined with only one other are at best simply not data science, or at worst downright dangerous.\n",
    "* For better or worse, data is a commodity traded electronically; therefore, in order to be in this market you need to speak hacker. This, however, does not require a background in computer science—in fact—many of the most impressive hackers I have met never took a single CS course. Being able to manipulate text files at the command-line, understanding vectorized operations, thinking algorithmically; these are the hacking skills that make for a successful data hacker.\n",
    "* Once you have acquired and cleaned the data, the next step is to actually extract insight from it. In order to do this, you need to apply appropriate math and statistics methods, which requires at least a baseline familiarity with these tools. This is not to say that a PhD in statistics in required to be a competent data scientist, but it does require knowing what an ordinary least squares regression is and how to interpret it.\n",
    "* In the third critical piece—substance—is where my thoughts on data science diverge from most of what has already been written on the topic. To me, data plus math and statistics only gets you machine learning, which is great if that is what you are interested in, but not if you are doing data science. Science is about discovery and building knowledge, which requires some motivating questions about the world and hypotheses that can be brought to data and tested with statistical methods. On the flip-side, substantive expertise plus math and statistics knowledge is where most traditional researcher falls. Doctoral level researchers spend most of their time acquiring expertise in these areas, but very little time learning about technology. Part of this is the culture of academia, which does not reward researchers for understanding technology. That said, I have met many young academics and graduate students that are eager to bucking that tradition.\n",
    "* Finally, a word on the hacking skills plus substantive expertise danger zone. This is where I place people who, \"know enough to be dangerous,\" and is the most problematic area of the diagram. In this area people who are perfectly capable of extracting and structuring data, likely related to a field they know quite a bit about, and probably even know enough R to run a linear regression and report the coefficients; but they lack any understanding of what those coefficients mean. It is from this part of the diagram that the phrase \"lies, damned lies, and statistics\" emanates, because either through ignorance or malice this overlap of skills gives people the ability to create what appears to be a legitimate analysis without any understanding of how they got there or what they have created. Fortunately, it requires near willful ignorance to acquire hacking skills and substantive expertise without also learning some math and statistics along the way. As such, the danger zone is sparsely populated, however, it does not take many to produce a lot of damage."
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   "source": [
    "## The Pi-shaped scientist"
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   "source": [
    "Introduced by Alex Szalay.\n",
    "![](figures/pi_shaped.png)"
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    "In the words of Alex Szalay, these sorts of researchers must be \"Pi-shaped\" as opposed to the more traditional \"T-shaped\" researcher. In Szalay's view, a classic PhD program generates T-shaped researchers: scientists with wide-but-shallow general knowledge, but deep skill and expertise in one particular area. The new breed of scientific researchers, the data scientists, must be Pi-shaped: that is, they maintain the same wide breadth, but push deeper both in their own subject area and in the statistical or computational methods that help drive modern research:"
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    "I detta sammanhang kan jag avslutningsvis nämna att det pågår ett intensivt arbete att skapa ett nytt mastersprogram i fysik (kommer att sjösättas hösten 2019)\n",
    "* som utnyttjar kunskapsbredden och problemlösarförmågan som finns hos dagens fysikstudenter (och teknisk matematik) \n",
    "* samt expertisen som finns hos lärarna, \n",
    "* där det fortfarande erbjuds möjlighet till fördjupning,\n",
    "* men där kursutbudet anpassas för att lära ut en uppdaterad uppsättning med verktyg och förmågor.\n",
    "\n",
    "Dvs en **Pi-formad** ingenjör!"
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