prob.predict {GSM}R Documentation

Tail probability estimation for a Gamma Shape Mixture Model

Description

This function allows to estimate the tail probability of a Gamma Shape Mixture Model using the output of the gsm or gsm.theta procedures.

Usage

   prob.predict(mcmc.w,mcmc.theta,thresh)

Arguments

mcmc.w matrix of the mixture's weights posterior draws; it is part of the output of the gsm or gsm.theta functions.
mcmc.theta vector of the mixture's rate parameter posterior draws; it is part of the output of the gsm or gsm.theta functions.
thresh threshold value.

Details

The tail probability is estimated by applying the standard Rao-Blackwellized estimator on the Gibbs sampling realizations obtained through the gsm or gsm.theta procedures.

Value

A numerical vector containing the posterior draws for the tail probability exceeding the value of thresh.

Author(s)

Sergio Venturini sergio.venturini@unibocconi.it

References

Venturini, S., Dominici, F., and Parmigiani, G., "Gamma Shape Mixtures for Heavy-Tailed Distributions" (December 2006). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 124. http://www.bepress.com/jhubiostat/paper124

See Also

gsm, gsm.plot.

Examples

set.seed(2040)
y <- rgsm(500,c(.1,.3,.4,.2),1)
burnin <- 100
J <- 250
gsm.out <- gsm(y,J,300,burnin+500,6500,340,1/J)
thresh <- c(0.1,0.5,0.75,1,2)
tail.prob.est <- rep(NA,length(thresh))
tail.prob.true <- rep(NA,length(thresh))
for (i in 1:length(thresh)){
   tail.prob.est[i] <- mean(prob.predict(gsm.out$weight[(burnin+1):600,],gsm.out$theta[(burnin+1):600],thresh[i]))
   tail.prob.true[i] <- sum(y>thresh[i])/length(y)
}
qqplot(tail.prob.true,tail.prob.est,main="Q-Q plot of true vs. estimated tail probability")
abline(0,1,lty=2)

[Package GSM version 0.1-2 Index]