gsm.theta {GSM}R Documentation

Estimation of a Gamma Shape Mixture Model (GSM)

Description

This function provides the inferential algorithm to estimate a mixture of gamma distributions in which the mixing occurs over the shape parameter. It implements the standard approach for the GSM model, as discussed in Venturini et al. (2006).

Usage

   gsm.theta(y,J,G,M,a,b,alpha)

Arguments

y vector of data.
J number of mixture components.
G number of points where to evaluate the GSM density.
M number of MCMC runs.
a hyperparameter of the rate parameter prior distribution.
b hyperparameter of the rate parameter prior distribution.
alpha hyperparameter of the mixture's weights prior distribution.

Details

Suggestions on how to choose J, a and b are provided in Venturini et al. (2006). In that work the alpha vector is always set at (1/J,...,1/J), but here one is free to choose the value of the generic element of alpha.

Value

List with the following components:

J number of mixture components used in the GSM model.
a hyperparameter of the rate parameter prior distribution used in the GSM model.
b hyperparameter of the rate parameter prior distribution used in the GSM model.
alpha hyperparameter of the mixture's weights prior distribution used in the GSM model.
ff matrix containing the posterior draws for the mixture's density.
y.grid vector of values used to evalute the GSM density.
theta vector containing the posterior draws for the mixture's rate parameter.
label matrix containing the posterior draws for the mixture's hidden label.
weight matrix containing the posterior draws for the mixture's weights.

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.theta(y,J,300,burnin+500,6500,340,1/J)
gsm.plot(gsm.out,y,ndens=0,nbin=20,histogram=TRUE)

[Package GSM version 0.1-2 Index]