From 4f95d4ef410bfdd2ada21ac7e7fca0b47bbac43f Mon Sep 17 00:00:00 2001 From: Francois Date: Mon, 19 Oct 2020 12:50:29 +0200 Subject: [PATCH 1/3] Adding link to develop branch --- .gitmodules | 3 +++ dev | 1 + 2 files changed, 4 insertions(+) create mode 100644 .gitmodules create mode 160000 dev diff --git a/.gitmodules b/.gitmodules new file mode 100644 index 0000000..ff56e5e --- /dev/null +++ b/.gitmodules @@ -0,0 +1,3 @@ +[submodule "Shear-and-PSF-Reading-Group"] + path = dev + url = https://github.com/CosmoStat/Shear-and-PSF-Reading-Group.git diff --git a/dev b/dev new file mode 160000 index 0000000..c507830 --- /dev/null +++ b/dev @@ -0,0 +1 @@ +Subproject commit c5078301d1afa4a8d480f036ccff8e62320afb1b From a6dfb0954699fd53279fe0d2cc0980ebb52ece99 Mon Sep 17 00:00:00 2001 From: Samuel Farrens Date: Fri, 27 Nov 2020 15:40:59 +0100 Subject: [PATCH 2/3] removed unused submodule --- .gitignore | 1 + .gitmodules | 3 --- dev | 1 - 3 files changed, 1 insertion(+), 4 deletions(-) delete mode 100644 .gitmodules delete mode 160000 dev diff --git a/.gitignore b/.gitignore index b6e4761..2386a80 100644 --- a/.gitignore +++ b/.gitignore @@ -9,6 +9,7 @@ __pycache__/ # Distribution / packaging .Python build/ +*_build* develop-eggs/ dist/ downloads/ diff --git a/.gitmodules b/.gitmodules deleted file mode 100644 index ff56e5e..0000000 --- a/.gitmodules +++ /dev/null @@ -1,3 +0,0 @@ -[submodule "Shear-and-PSF-Reading-Group"] - path = dev - url = https://github.com/CosmoStat/Shear-and-PSF-Reading-Group.git diff --git a/dev b/dev deleted file mode 160000 index c507830..0000000 --- a/dev +++ /dev/null @@ -1 +0,0 @@ -Subproject commit c5078301d1afa4a8d480f036ccff8e62320afb1b From 8e7e59c65f04f21a602084b8991e1cc2d1a6072f Mon Sep 17 00:00:00 2001 From: b-remy Date: Tue, 8 Dec 2020 20:10:17 +0100 Subject: [PATCH 3/3] add freq bayes estimator notebook --- Frequentist_or_Bayesian_estimator.ipynb | 303 ++++++++++++++++++++++++ 1 file changed, 303 insertions(+) create mode 100644 Frequentist_or_Bayesian_estimator.ipynb diff --git a/Frequentist_or_Bayesian_estimator.ipynb b/Frequentist_or_Bayesian_estimator.ipynb new file mode 100644 index 0000000..848baf9 --- /dev/null +++ b/Frequentist_or_Bayesian_estimator.ipynb @@ -0,0 +1,303 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Frequentist of Bayesian measurement?\n", + "This notebook aims to understand the different behavior between a likelihood and a bayesian estimator, and in particular their *bias*. It reproduces the example illustred in the *Galaxy Shape Measurment* paper [Miller et al.](https://arxiv.org/pdf/0708.2340.pdf), Figure 1.\n", + "\n", + "The authors used a Bayesian estimator for their model-fitting algorithm, arguing that **for a given set of measurements the Bayesian estimator yields the best estimate of the input values**. They illustrated this point with the following example.\n", + "\n", + "Let us consider a Bayesian estimator $\\hat{x}_{\\mathcal{B}} = \\int x p(x|y) dx$ and a Likelihood estimator $\\hat{x}_{\\mathcal{L}} = \\int x \\mathcal{L}(y|x) dx$ (mean posterior and mean likelihood estimators).\n", + "\n", + "Let us assume that: \n", + "- the intrinsic distribution of $x$ has a normal distribution of variance $a^2$, i.e. $x\\sim\\mathcal{N}(0, a^2)$ (*prior*),\n", + "- for each $x$ drawn from this distribution the measurement process causes a normally distributed uncertainty of variance $b^2$, i.e. $y|x \\sim \\mathcal{N}(x, b^2)$ (*likelihood*).\n", + "\n", + "Then we can easily compute the *posterior* distribution $p(x|y)$ using the Bayes formula: $p(x|y)=\\dfrac{\\mathcal{L}(y|x)p(x)}{\\int \\mathcal{L}(y|x')p(x')dx'}$\n", + "\n", + "The results are obtained in a Monte Carlo realisation for the illustrative case $a=0.3$ and $b=0.4$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "a = 0.3\n", + "b = 0.4\n", + "\n", + "# parameter to estimate x (e.g. galaxy intrinsic properties) x ~ N(0, a^2)\n", + "x_input = np.random.normal(loc=0, scale=a, size=10000)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# measurments (observations) from which we want to fit the parameters y|x ~ N(x, b^2)\n", + "y = np.random.normal(loc=x_input, scale=b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For each $x_\\text{input}$, compute its likelihood $\\hat{x}_\\mathcal{L}$ and bayesian $\\hat{x}_\\mathcal{B}$ estimate with the *Monte Carlo method*.\n", + "\n", + "[Monte Carlo Method](http://ib.berkeley.edu/labs/slatkin/eriq/classes/guest_lect/mc_lecture_notes.pdf): The expected value of a function $g$ of a random variable $X$, i.e. $\\mathbb{E}[g(X)] = \\int g(x) f_X(x) dx$ (where $f_X$ is the p.d.f. of $X$), can be approximated by the mean of $g(x)$ over samples of $X$, i.e. $x\\sim X$.\n", + "\n", + "In other words $$\\tilde{g}_n(X) = \\dfrac{1}{n}\\sum_{i=1}^n g(x_i),$$ where the $x_{i\\in [[1, n]]}$ are samples from $X$ with p.d.f. $f_X$, is the *Monte Carlo estimate* of $\\mathbb{E}[g(X)] = \\int g(x) f_X(x) dx$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example we can analyticaly compute the likelihood $\\mathcal{L}(y|x)$ and the posterior $p(x|y)$ distributions:\n", + "- *likelihood*: $y|x \\sim \\mathcal{N}\\left(x, b^2\\right)$\n", + "- *posterior*: $x|y \\sim \\mathcal{N}\\left(y\\dfrac{a^2}{a^2+b^2}, \\dfrac{a^2+b^2}{a^2 b^2}\\right)$ (intermediary result: $y\\sim \\mathcal{N}\\left(0, \\frac{1}{a^2+b^2}\\right)$)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "n = 10000\n", + "\n", + "# Likelihood estimator\n", + "xi_L = np.random.normal(loc=y, scale=b, size= (n, y.shape[0])) # sample the x_is\n", + "x_L = np.mean(xi_L, axis=0) # Monte Carlo average g = identity\n", + "\n", + "# Bayesian estimator\n", + "xi_B = np.random.normal(loc=y*(a**2)/(a**2+b**2), scale=np.sqrt((a**2+b**2))/a*b, size=(n, y.shape[0]))\n", + "x_B = np.mean(xi_B, axis=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Visualizing the results" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Input w.r.t. likelihood estimation: reg coef 0.36 => biased\n", + "Likelihood estimation w.r.t. input: reg coef 1.01 => unbiased\n", + "Input w.r.t. Bayesian estimation: reg coef 0.99 => unbiased\n", + "Bayesian estimation w.r.t. input: reg coef 0.36 => biased\n" + ] + } + ], + "source": [ + "from sklearn.linear_model import LinearRegression\n", + "\n", + "x_input = x_input.reshape(-1, 1)\n", + "x_L = x_L.reshape(-1, 1)\n", + "x_B = x_B.reshape(-1, 1)\n", + "\n", + "reg_L_estimate = LinearRegression().fit(x_L, x_input)\n", + "print(\"Input w.r.t. likelihood estimation: reg coef {:.2f} => biased\".format(reg_L_estimate.coef_[0][0]))\n", + "\n", + "reg_L_input = LinearRegression().fit(x_input, x_L)\n", + "print(\"Likelihood estimation w.r.t. input: reg coef {:.2f} => unbiased\".format(reg_L_input.coef_[0][0]))\n", + "\n", + "reg_B_estimate = LinearRegression().fit(x_B, x_input)\n", + "print(\"Input w.r.t. Bayesian estimation: reg coef {:.2f} => unbiased\".format(reg_B_estimate.coef_[0][0]))\n", + "\n", + "reg_B_input = LinearRegression().fit(x_input, x_B)\n", + "print(\"Bayesian estimation w.r.t. input: reg coef {:.2f} => biased\".format(reg_B_input.coef_[0][0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As Miller et al. concluded, we observe that\n", + "- For a given input value, the likelihood estimator yields an unbiased estimate (regression slope unity) whereas the Bayesian estimator appears biased (regression slope 0.35).\n", + "- For a given estimated value, the likelihood estimator is biased (regression slope 0.36) and the Bayesian estimator is unbiased." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(13, 5))\n", + "plt.subplots_adjust(wspace = .3)\n", + "\n", + "plt.subplot(121)\n", + "plt.scatter(x_L, x_input, marker=\".\", c='black', s=1)\n", + "plt.plot([-2.5, 2.5], [-2.5*reg_L_estimate.coef_[0][0], 2.5*reg_L_estimate.coef_[0][0]], linewidth=2, label=\"$x_{input}~\\mathrm{w.r.t.}~\\hat{x}_{\\mathcal{L}}$\")\n", + "plt.plot([-2.5*reg_L_input.coef_[0][0], 2.5*reg_L_input.coef_[0][0]], [-2.5, 2.5], linewidth=2, label=\"$\\hat{x}_{\\mathcal{L}}~\\mathrm{w.r.t.}~x_{input}$\")\n", + "plt.xlabel(\"$\\hat{x}_\\mathcal{L}$\", fontsize=15)\n", + "plt.ylabel(\"$x_{input}$\", fontsize=15)\n", + "plt.xlim(-1.5, 1.5)\n", + "plt.ylim(-1.5, 1.5)\n", + "plt.axis(\"equal\")\n", + "plt.legend()\n", + "\n", + "plt.subplot(122)\n", + "plt.scatter(x_B, x_input, marker=\".\", c='black', s=1)\n", + "plt.plot([-2.5, 2.5], [-2.5*reg_B_estimate.coef_[0][0], 2.5*reg_B_estimate.coef_[0][0]], linewidth=2, label=\"$x_{input}~\\mathrm{w.r.t.}~\\hat{x}_{\\mathcal{B}}$\")\n", + "plt.plot([-2.5*reg_B_input.coef_[0][0], 2.5*reg_B_input.coef_[0][0]], [-2.5, 2.5], linewidth=2, label=\"$\\hat{x}_{\\mathcal{B}}~\\mathrm{w.r.t.}~x_{input}$\")\n", + "plt.xlabel(\"$\\hat{x}_\\mathcal{B}$\", fontsize=15)\n", + "plt.ylabel(\"$x_{input}$\", fontsize=15)\n", + "plt.xlim(-1.5, 1.5)\n", + "plt.ylim(-1.5, 1.5)\n", + "plt.axis(\"equal\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(13, 5))\n", + "plt.subplots_adjust(wspace = .3)\n", + "plt.subplot(121)\n", + "plt.scatter(x_L, x_input-x_L, marker=\".\", c='black')\n", + "plt.xlabel(\"$\\hat{x}_\\mathcal{L}$\", fontsize=15)\n", + "plt.ylabel(\"$x_{input} - \\hat{x}_\\mathcal{L}$\", fontsize=15)\n", + "plt.xlim(-1.5, 1.5)\n", + "plt.ylim(-1.5, 1.5)\n", + "plt.axis(\"equal\")\n", + "plt.subplot(122)\n", + "plt.scatter(x_B, x_input-x_B, marker=\".\", c='black')\n", + "plt.xlabel(\"$\\hat{x}_\\mathcal{B}$\", fontsize=15)\n", + "plt.ylabel(\"$x_{input} - \\hat{x}_\\mathcal{B}$\", fontsize=15)\n", + "plt.xlim(-1.5, 1.5)\n", + "plt.ylim(-1.5, 1.5)\n", + "plt.axis(\"equal\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(13, 5))\n", + "plt.subplots_adjust(wspace = .3)\n", + "plt.subplot(121)\n", + "plt.scatter(x_input, x_input-x_L, marker=\".\", c='black')\n", + "plt.xlabel(\"$x_{input}$\", fontsize=15)\n", + "plt.ylabel(\"$x_{input} - \\hat{x}_\\mathcal{L}$\", fontsize=15)\n", + "plt.xlim(-1.5, 1.5)\n", + "plt.ylim(-1.5, 1.5)\n", + "plt.axis(\"equal\")\n", + "plt.subplot(122)\n", + "plt.scatter(x_input, x_input-x_B, marker=\".\", c='black')\n", + "plt.xlabel(\"$x_{input}$\", fontsize=15)\n", + "plt.ylabel(\"$x_{input} - \\hat{x}_\\mathcal{B}$\", fontsize=15)\n", + "plt.xlim(-1.5, 1.5)\n", + "plt.ylim(-1.5, 1.5)\n", + "plt.axis(\"equal\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "cosmo", + "language": "python", + "name": "cosmo" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}