posteriorMCMC {ExtremalDep} | R Documentation |
Generates a sample from the posterior distribution for the parameters and computes the posterior mean, component-wise variance and BIC.
posteriorMCMC(Nsim, Nbin=0, Hpar, MCpar, dat, par.start=NULL, show.progress=floor(seq(1,Nsim, length.out=20)), seed=NULL, kind="Mersenne-Twister", save=FALSE, name.save=NULL, save.directory = "~", name.dat="", model, c=NULL)
Nsim |
Total number of iterations to perform. |
Nbin |
Length of the burn-in period. |
Hpar |
A vector of hyper-parameters. See prior. |
MCpar |
MC MC parameter.See proposal. |
dat |
Angular dataset. Each row corresponds to coordinates in the simplex. |
par.start |
Starting point for the MC MC sample. |
show.progress |
A vector of integers containing the times (iteration numbers) at which a message showing progression will be printed on the standard output. |
seed |
The seed to be set via the routine set.seed, see help of R for details. |
kind |
The kind of random number generator. Default is |
save |
Logical; if |
name.save |
A character string giving the name under which the result is to be saved. If |
save.directory |
A character string giving the directory where the result is to be saved (without trailing slash). |
name.dat |
A character string naming the dataset used for inference. Default is "". |
model |
A character string. Possible models are |
c |
A real value in [0,1], providing the decision rule to allocate a data point to a subset of the simplex. Only required for the Extremal-t and Asymmetric Logistic models. |
When model="Pairwise"
the Pairiwse Beta model is selected and prior.pb
, proposal.pb
, pb.Hpar
, pb.MCpar
are considered. Similarly model="Husler"
selects the Husler-Reiss model,
model="Dirichlet"
the Tilted Dirichlet model, model="Extremalt"
the Extremal-t and model="Asymmetric"
the Asymmetric Logistic model and the functions associated to these models.
A list made of
stored.vales |
A (Nsim-Nbin)*d matrix, where d is the dimension of the parameter space |
llh |
A vector of size (Nsim-Nbin) containing the log-likelihoods evaluadted at each parameter of the posterior sample. |
lprior |
A vector of size (Nsim-Nbin) containing the logarithm of the prior densities evaluated at each parameter of the posterior sample. |
elapsed |
The time elapsed, as given by |
Nsim |
The same as the passed argument. |
Nbin |
Idem. |
n.accept |
The total number of accepted proposals. |
n.accept.kept |
The number of accepted proposals after the burn-in period. |
emp.mean |
The estimated posterior parameters mean. |
emp.sd |
The empirical posterior sample standard deviation. |
BIC |
The Bayesian Information Criteria. |
Simone Padoan, simone.padoan@unibocconi.it, http://faculty.unibocconi.it/simonepadoan; Boris Beranger, borisberanger@gmail.com http://www.borisberanger.com;
################################################ # The following examples provide the results of # the approximate bayesian analysis in Table 1.1 # of the paper Beranger and Padoan (2015) ################################################ ## Load datasets : data(pollution) Nsim <- 50e+4 Nbin <- 30e+4 MCpar <- 0.35 Hpar.pb <- list(mean.alpha=0, mean.beta=3,sd.alpha=3, sd.beta=3) Hpar.hr <- list(mean.lambda=0, sd.lambda=3) Hpar.di <- list(mean.alpha=0, sd.alpha=3) Hpar.et <- list(mean.rho=0, mean.mu=3,sd.rho=3, sd.mu=3) ## Using the PNS dataset est.pb.PNS <- posteriorMCMC(Nsim, Nbin, Hpar.pb, MCpar, PNS, seed=14342, model='Pairwise') est.pb.PNS$emp.mean est.pb.PNS$emp.sd est.pb.PNS$BIC est.hr.PNS <- posteriorMCMC(Nsim, Nbin, Hpar.hr, MCpar, PNS, seed=14342, model='Husler') est.hr.PNS$emp.mean est.hr.PNS$emp.sd est.hr.PNS$BIC est.di.PNS <- posteriorMCMC(Nsim, Nbin, Hpar.di, MCpar, PNS, seed=14342, model='Dirichlet') est.di.PNS$emp.mean est.di.PNS$emp.sd est.di.PNS$BIC est.et.PNS <- posteriorMCMC(Nsim, Nbin, Hpar.et, MCpar, PNS, seed=14342, model='Extremalt',c=0.1) est.et.PNS$emp.mean est.et.PNS$emp.sd est.et.PNS$BIC ## Using the NSN dataset est.pb.NSN <- posteriorMCMC(Nsim, Nbin, Hpar.pb, MCpar, NSN, seed=14342, model='Pairwise') est.pb.NSN$emp.mean est.pb.NSN$emp.sd est.pb.NSN$BIC est.hr.NSN <- posteriorMCMC(Nsim, Nbin, Hpar.hr, MCpar, NSN, seed=14342, model='Husler') est.hr.NSN$emp.mean est.hr.NSN$emp.sd est.hr.NSN$BIC est.di.NSN <- posteriorMCMC(Nsim, Nbin, Hpar.di, MCpar, NSN, seed=14342, model='Dirichlet') est.di.NSN$emp.mean est.di.NSN$emp.sd est.di.NSN$BIC est.et.NSN <- posteriorMCMC(Nsim, Nbin, Hpar.et, MCpar, NSN, seed=14342, model='Extremalt',c=0.1) est.et.NSN$emp.mean est.et.NSN$emp.sd est.et.NSN$BIC ## Using the PNN dataset est.pb.PNN <- posteriorMCMC(Nsim, Nbin, Hpar.pb, MCpar, PNN, seed=14342, model='Pairwise') est.pb.PNN$emp.mean est.pb.PNN$emp.sd est.pb.PNN$BIC est.hr.PNN <- posteriorMCMC(Nsim, Nbin, Hpar.hr, MCpar, PNN, seed=14342, model='Husler') est.hr.PNN$emp.mean est.hr.PNN$emp.sd est.hr.PNN$BIC est.di.PNN <- posteriorMCMC(Nsim, Nbin, Hpar.di, MCpar, PNN, seed=14342, model='Dirichlet') est.di.PNN$emp.mean est.di.PNN$emp.sd est.di.PNN$BIC est.et.PNN <- posteriorMCMC(Nsim, Nbin, Hpar.et, MCpar, PNN, seed=14342, model='Extremalt',c=0.1) est.et.PNN$emp.mean est.et.PNN$emp.sd est.et.PNN$BIC ################################################ # The following examples provide the results of # the approximate bayesian analysis in Table 1.2 # of the paper Beranger and Padoan (2015) ################################################ # Using the PNNS dataset est.pb.PNNS <- posteriorMCMC(Nsim, Nbin, Hpar.pb, MCpar, PNNS, seed=14342, model='Pairwise') est.pb.PNNS$BIC est.hr.PNNS <- posteriorMCMC(Nsim, Nbin, Hpar.hr, MCpar, PNNS, seed=14342, model='Husler') est.hr.PNNS$BIC est.di.PNNS <- posteriorMCMC(Nsim, Nbin, Hpar.di, MCpar, PNNS, seed=14342, model='Dirichlet') est.di.PNNS$BIC