Mixtures of mutually singular distributions let Bayesian variable selection run in ordinary fixed-dimensional MCMC while matching the spike-and-slab posterior and RJMCMC acceptance probabilities.
In each case, the parameter space is partitioned into exclusive subspaces, and posterior inference proceeds across those subspaces rather than within a single unconstrained model
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Reversible Jump MCMC With No Regrets: Bayesian Variable Selection Using Mixtures of Mutually Singular Distributions
Mixtures of mutually singular distributions let Bayesian variable selection run in ordinary fixed-dimensional MCMC while matching the spike-and-slab posterior and RJMCMC acceptance probabilities.