SMPracticals (version 1.4-3.1)

exp.gibbs: Gibbs Sampling for Two Truncated Exponential Variables, Practical 11.3

Description

Performs Gibbs sampling for problem with two truncated exponential variables. See Practical 11.3 of Davison (2003) for details.

Usage

exp.gibbs(u1 = NULL, u2 = NULL, B, I = 100, S = 100)

Value

A 2 x S x I array containing the values of the variables for the successive iterations

Arguments

u1

Initial values for variable 1

u2

Initial values for variable 2

B

Value at which exponential distribution is truncated

I

Number of iterations of sampler

S

Number of replicates of sampler

Author

Anthony Davison ([e-mail])

Details

This is provided simply so that readers spend less time typing. It is not intended to be robust and general code.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press.Practical 11.3.

Examples

add.exp.lines <- function( exp.out, i, B=10)
{
  dexp.trunc <- function( u, lambda, B ) 
     dexp(u, rate=lambda)/(1-exp(-lambda*B))
  S <- dim(exp.out)[2]
  I <- dim(exp.out)[3]
  u <- seq(0.0001,B,length=1000)
  fu <- rep(0,1000)
  for (s in 1:S) fu <- fu + dexp.trunc(u,exp.out[3-i,s,I],B)/S
  lines(u,fu,col="red")
  invisible()
}
par(mfrow=c(3,2))
B <-10; I <- 15; S <- 500
exp.out <- exp.gibbs(B=B,I=I,S=S)
hist(exp.out[1,,I],prob=TRUE,nclass=15,xlab="u1",ylab="PDF",xlim=c(0,B),ylim=c(0,1))
add.exp.lines(exp.out,1)
hist(exp.out[2,,I],prob=TRUE,nclass=15,xlab="u2",ylab="PDF",xlim=c(0,B),ylim=c(0,1))
add.exp.lines(exp.out,2)