hus.gibbs: Gibbs Sampler for Poisson Changepoint Model, Practical 11.6
In SMPracticals: Practicals for Use with Davison (2003) Statistical Models

Description Usage Arguments Details Value Author(s) References Examples

This function implements a Gibbs sampler for the Poisson changepoint model applied to the HUS data used in Example 4.40 and Practical 11.6 of Davison (2003), which should be consulted for details.

1	hus.gibbs(init, y, R = 10, a1 = 1, a2 = 1, c = 0.01, d = 0.01)

`init`	Initial values for parameters
`y`	A series of Poisson counts
`R`	Number of iterations of sampler
`a1`	Value of a hyperparameter
`a2`	Value of a hyperparameter
`c`	Value of a hyperparameter
`d`	Value of a hyperparameter

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

A matrix of size R x 7, whose first five columns contain the values of the parameters for the iterations. Columns 6 and 7 contain the log likelihood and log prior for that iteration.

Anthony Davison (anthony.davison@epfl.ch)

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Practical 11.6.

## From Example 11.6:
hus <- c(1,5,3,2,2,1,0,0,2,1,1,7,11,4,7,10,16,16,9,15)
system.time( gibbs.out <- hus.gibbs(c(5, 5, 1, 1, 2), hus, R=1000))
plot.ts(gibbs.out[,1], main="lambda1") # time series plot for lam1
plot.ts(gibbs.out[,2], main="lambda1") # time series plot for lam2
plot.ts(gibbs.out[,6], main="log lik") # and of log likelihood
table(gibbs.out[,5])  # tabulate observed values of tau
rm(hus)