  Bayesian model selection, with precedents in George and McCulloch (1993) and
Abramovich et al. (1998), support credibility measures that relate model
uncertainty, but computation can be costly when sparse priors are approximate.
We design an exact selection engine suitable for Gauss noise, t-distributed
noise, and logistic learning, benefiting from data-structures derived from
coordinate descent lasso. Gibbs sampler chains are stored in a compressed
binary format compatible with Equi-Energy (Kou et al., 2006) tempering. We
achieve a grouped-effects selection model, similar to the setting for group
lasso, to determine co-entry of coefficients into the model. We derive a
functional integrand for group inclusion, and introduce a new MCMC switching
step to avoid numerical integration. Theorems show this step has exponential
convergence to target distribution. We demonstrate a role for group selection
to inform on genetic decomposition in a diallel experiment, and identify
potential quantitative trait loci in p > 40K Heterogenous Stock
haplotype/phenotype studies.
