spikeAndSlab: Set up and sample a spike-and-slab prior model.

Description

This function sets up a spike-and-slab model for variable selection and model choice in generalized additive models and samples its posterior. It uses a blockwise Metropolis-within-Gibbs sampler and the redundant multiplicative parameter expansion described in the reference. This routine is not meant to be called directly by the user -- spikeSlabGAM provides a formula-based interface for specifying models and takes care of (most of) the housekeeping. Sampling of the chains is done in parallel using package parallel. A "SOCK" cluster is set up under Windows to do so (and closed after computations are done, I try to clean up after myself), see makeCluster etc. Use options(mc.cores=) to set the (maximal) number of processes forked by the parallelization. If options()$mc.cores is unspecified, it is set to 2.

Usage

spikeAndSlab(y, X,
    family = c("gaussian", "binomial", "poisson"),
    hyperparameters = list(), model = list(),
    mcmc = list(), start = list())

Arguments

response

design matrix

family

(character) the family of the response, defaults to normal/Gaussian response

hyperparameters

a list of hyperparameters controlling the priors (see details)

model

a list with information about the grouping structure of the model (see details)

mcmc

(optional) list setting arguments for the sampler (see details)

start

(optional) list containing the starting values for $\beta, \gamma, \tau^2, \sigma^2, w$ and, optionally, the random seed

Value

a list with components:[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Details

Details for model specification: [object Object],[object Object],[object Object],[object Object]

References

Scheipl, F. (2010) Normal-Mixture-of-Inverse-Gamma Priors for Bayesian Regularization and Model Selection in Structured Additive Regression Models. LMU Munich, Department of Statistics: Technical Reports, No.84 (http://epub.ub.uni-muenchen.de/11785/)