bf2 {bspmma}

Compute Constants for Multi-Chain Algorithm to Compute Bayes Factors

Description

This function computes nine constants needed in the multi-chain algorithm for Bayes factors comparing conditional and ordinary Dirichlet mixing models, and for Bayes factors comparing Dirichlet precision parameter (M) values for the conditional model, or for the ordinary model.

Usage

bf2(chain.list)

Arguments

chain.list

is a list of nine matrices of MCMC output produced by function bf1

Details

This function computes the constants needed for the denominator of the left-side of Eqn. (2.5) of Doss (2012). This is the step in which Radon-Nikodym derivatives are evaluated for each line of MCMC output and then averaged to estimate the constants. The actual algorithm is a little more complicated than that to make use of output from multiple chains. Nine constants are computed in this way.

Value

A vector of nine constants which is needed in the next step of the computation of the Bayes factors. Burr (2012) gives detailed explanations of the algorithm and illustrates the steps in the algorithm.

References

Burr, Deborah (2012). “bspmma: An R package for Bayesian semi-parametric models for meta-analysis.” Journal of Statistical Software 50(4), 1–23. http://www.jstatsoft.org/v50/i04/.

Doss, Hani (2012). “Hyperparameter and model selection for nonparametric Bayes problems via Radon-Nikodym derivatives.” Statistica Sinica, 22, 1–26.

Examples

## Not run: 
## Get the two sets of chains saved from runs of bf1 from
## the breast cancer example in the help file for bf1.
load("breast-rdat-2lists-1000")

## Default values ncycles=2000, burnin=1000
##  CPU time is from a run of the R command system.time() on an
##  Intel $2.8$ GHz Q$9550$ running Linux.
cc <- bf2(chain1.list) #1.6 secs

## Perhaps save for another time.
save(cc,file="breast-rdat-constants",compress=TRUE)

## Next session
load("breast-rdat-constants")


## End(Not run)