GSM (version 1.3.2)

predict-methods: Tail Probability Estimation for a Gamma Shape Mixture Model

Description

predict method for class "gsm". This function allows to estimate the tail probability of a Gamma Shape Mixture Model using the output of the estim.gsm or estim.gsm_theta procedures.

Usage

"predict"(object, thresh, start = 1, ...)

Arguments

object

object of class "gsm"; a list returned by the estim.gsm or estim.gsm_theta functions.

thresh

threshold value.

start

MCMC run to start from.

...

further arguments passed to or from other methods.

Value

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

Details

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

References

Venturini, S., Dominici, F. and Parmigiani, G. (2008), "Gamma shape mixtures for heavy-tailed distributions". Annals of Applied Statistics, Volume 2, Number 2, 756--776. http://projecteuclid.org/euclid.aoas/1215118537

See Also

estim.gsm, estim.gsm_theta, predict-methods, plot-methods.

Examples

set.seed(2040)
y <- rgsm(500, c(.1, .3, .4, .2), 1)
burnin <- 5
mcmcsim <- 10
J <- 250
gsm.out <- estim.gsm(y, J, 300, burnin + mcmcsim, 6500, 340, 1/J)
thresh <- c(0.1, 0.5, 0.75, 1, 2)
tail.prob.est <- tail.prob.true <- rep(NA, length(thresh))
for (i in 1:length(thresh)){
   tail.prob.est[i] <- mean(predict(gsm.out, 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)