April 2010
In variable selection problems that preclude enumeration of models, stochastic search algorithms, often based on Markov Chain Monte Carlo, are commonly used to identify a set of models for model selection or model averaging. Because Monte Carlo frequencies of models are often zero or one in high dimensional problems, posterior probabilities calculated from the observed marginal likelihoods, re-normalized over the sampled models are often employed. Such estimates are the only recourse in the newer generation of stochastic search algorithms. In this paper, we show that the approach of estimating model probabilities based on renormalization of posterior probabilities over the set of sampled models leads to bias in many quantities of interest and may not reduce mean squared error.
Keywords: Bayesian model averaging; Inclusion probability, Markov chain Monte Carlo; Median probability model; Model uncertainty; Variable Selection
The manuscript is available in PDF formats.