gsm.theta {GSM} | R Documentation |
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).
gsm.theta(y,J,G,M,a,b,alpha)
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. |
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
.
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. |
Sergio Venturini sergio.venturini@unibocconi.it
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
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)