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We show that a probabilistic version of the classical forward-stepwisevariable inclusion procedure can serve as a general data-augmentation schemefor model space distributions in (generalized) linear models. This latentvariable representation takes the form of a Markov process, thereby allowinginformation propagation algorithms to be applied for sampling from model spaceposteriors. In particular, we propose a sequential Monte Carlo method forachieving effective unbiased Bayesian model averaging in high-dimensionalproblems, utilizing proposal distributions constructed using local informationpropagation. We illustrate our method---called LIPS for local informationpropagation based sampling---through real and simulated examples withdimensionality ranging from 15 to 1,000, and compare its performance inestimating posterior inclusion probabilities and in out-of-sample prediction tothose of several other methods---namely, MCMC, BAS, iBMA, and LASSO. Inaddition, we show that the latent variable representation can also serve as amodeling tool for specifying model space priors that account for knowledgeregarding model complexity and conditional inclusion relationships.

Scalable Bayesian model averaging through local information propagation