Journal article
Finite population estimators in stochastic search variable selection
Biometrika, Vol.99(4), pp.981-988
2012
DOI: 10.1093/biomet/ass040
Abstract
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.
Details
- Title: Subtitle
- Finite population estimators in stochastic search variable selection
- Creators
- Merlise A ClydeJoyee Ghosh
- Resource Type
- Journal article
- Publication Details
- Biometrika, Vol.99(4), pp.981-988
- DOI
- 10.1093/biomet/ass040
- ISSN
- 0006-3444
- eISSN
- 1464-3510
- Language
- English
- Date published
- 2012
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9983985951702771
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