Finite population estimators in stochastic search variable selection

Journal Article (Journal Article)

Monte Carlo algorithms are commonly used to identify a set of models for Bayesian model selection or model averaging. Because empirical frequencies of models are often zero or one in high-dimensional problems, posterior probabilities calculated from the observed marginal likelihoods, renormalized over the sampled models, are often employed. Such estimates are the only recourse in several newer stochastic search algorithms. In this paper, we prove that renormalization of posterior probabilities over the set of sampled models generally leads to bias that may dominate mean squared error. Viewing the model space as a finite population, we propose a new estimator based on a ratio of Horvitz-Thompson estimators that incorporates observed marginal likelihoods, but is approximately unbiased. This is shown to lead to a reduction in mean squared error compared to the empirical or renormalized estimators, with little increase in computational cost. © 2012 Biometrika Trust.

Full Text

Duke Authors

Cited Authors

  • Clyde, MA; Ghosh, J

Published Date

  • December 1, 2012

Published In

Volume / Issue

  • 99 / 4

Start / End Page

  • 981 - 988

Electronic International Standard Serial Number (EISSN)

  • 1464-3510

International Standard Serial Number (ISSN)

  • 0006-3444

Digital Object Identifier (DOI)

  • 10.1093/biomet/ass040

Citation Source

  • Scopus