diff --git a/index.html b/index.html new file mode 100644 index 0000000..77392de --- /dev/null +++ b/index.html @@ -0,0 +1,737 @@ + + + + + + CircSpaceTime: An R package for spatial, spatio-temporal and temporal model for circular, cylindrical and spherical data + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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CircSpaceTime: An R package for spatial, spatio-temporal and temporal model for circular, cylindrical and spherical data

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+github.com/santoroma/CircSpaceTime +23rd International Conference on Computational Statistics

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A brand new package

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A brand new package

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  • Currently the following models are implemented:

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    • Spatial Wrapped Normal
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    • Spatial Projected Normal
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  • Yet to come (in few weeks):

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    • Spatio-Temporal Wrapped Normal
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    • Spatio-Temporal Projected Normal
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A brand new package

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  • Already available on GitHub at github.com/santoroma/CircSpaceTime
    +The package will be released on CRAN before the end of the 2018.

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  • It will be constantly updated with Bayesian and classical models dealing with complex dependence structures for circular, cylindrical and spherical variable.

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A brief example

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  • Example based on wave directions (and heights): a storm event observed at 8pm of April 6, 2010.

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  • Data available inside the package.

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Test data

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We hold out 10% of the locations for validation purposes

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Estimation based on the Wrapped Gaussian

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WrapSp

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  • WrapSp function produces samples from the Wrapped Normal spatial model posterior distribution
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  • As inputs it requires:

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    • a vector of \(n\) circular data in \([0,2\pi)\) and a matrix of coordinates (train data in our example)
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    • two lists, one of starting values for the MCMC and the other for the prior distributions definition.
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    • Further inputs are related to computational options such as the number of chains, if the computation should be parallelized and the number of iterations.
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+
 storm <- WrapSp(
+ x     = train0$Dmr,
+ coords    = coords0.train,
+ start   = start0 ,
+ prior   = list("alpha"      = c(pi,10), 
+ "rho"     = c(rho_min0, rho_max0), 
+ "sigma2"    = c(3,0.5),
+ "beta"      = c(1,1,2)  
+ ) ,
+ nugget = TRUE,
+ sd_prop   = list( "sigma2" = 1, "rho" = 0.3, "beta" = 1),
+ iter    = 30000,
+  bigSim    = c(burnin = 15000, thin = 10),
+ accept_ratio = 0.5,
+ adapt_param = c(start = 1000, end = 10000, esponente = 0.95),
+ corr_fun = "exponential", 
+ n_chains = 2,
+ parallel = T,
+ n_cores = 2)
+

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WrapKrig

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  • WrapKrig function estimate the values on the test sites using the posterior samples we just obtained
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  • As inputs it requires:

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    • the output of WrapSp
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    • the coordinates for the train (observed) points
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    • the coordinates of the test (validation) points
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    • the observed (train) circular values
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 Pred.storm <- WrapKrig(
+   WrapSp_out = storm,
+## The coordinates for the observed points
+  coords_obs = coords0.train,
+## The coordinates of the validation points
+  coords_nobs = coords0.test,
+##the observed circular values
+   x_oss = train0$Dmr
+ )
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Estimation based on the Projected Gaussian

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ProjSp

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  • ProjSp function produces samples from the Projected Normal spatial model posterior distribution
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  • As inputs it requires:

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    • a vector of \(n\) circular data in \([0,2\pi)\) and a matrix of coordinates (train data in our example)
      • +
    • two lists, one of starting values for the MCMC and the other for the prior distributions definition.
      • +
    • Further inputs are related to computational options such as the number of chains, if the computation should be parallelized and the number of iterations.
      • +
    • +
+
 mod0_PN <- ProjSp(
+  x     = train0$Dmr,
+  coords    = coords0.train,
+  start   = start0_PN ,
+  prior   = list("alpha_mu"      = c(0,0),
+                 "alpha_sigma"   = diag(10,2),
+                 "rho0"     = c(rho_min0, rho_max0),
+                 "rho"      = c(-1,1),
+                 "sigma2"    = c(3,0.5)),
+  sd_prop   = list( "sigma2" = .1, "rho0" = 0.1, "rho" = .1,  "sdr" = sample(.05,length(train0$Dmr), replace = T)),
+  iter    = 5000,
+  bigSim    = c(burnin = 3500, thin = 1),
+  accept_ratio = 0.5,
+  adapt_param = c(start = 1000, end = 10000, esponente = 0.95, sdr_update_iter = 50),
+  corr_fun = "exponential", 
+  n_chains = 2,
+  parallel = T,
+  n_cores = 2)
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ProjKrig

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  • ProjKrig function estimate the values on the test sites using the posterior samples we just obtained
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  • As inputs it requires:

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    • the output of ProjSp
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      • +
    • the coordinates for the train (observed) points
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    • the coordinates of the test (validation) points
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    • the observed (train) circular values
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+
 Pred.krig_PN <- ProjKrig(mod0_PN,
+                      ## The coordinates for the observed points  
+                      coords_obs = coords0.train,
+                      ## The coordinates of the validation points
+                      coords_nobs = coords0.test,
+                      ##the observed circular values
+                      x_oss = train0$Dmr)
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Comparison

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  • We can compare the predictions of the two models using the Average Prediction Error (APE)
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  • It’s the package function APEcirc


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WrappedProjected
Average Prediction Error0.00070.0010
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 APE_WRAP <- APEcirc( real = test0$Dmr,
+                sim = Pred.storm$Prev_out,
+                bycol = F
+)
+  APE_PN <- APEcirc( real = test0$Dmr,
+                sim = Pred.krig_PN$Prev_out,
+                bycol = F
+)
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… this is the END

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THANKS!!!

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Further information and installation instructions on github.com/santoroma/CircSpaceTime

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