Investigation of the widely applicable Bayesian information criterion

Publisher:
Springer
Publication Type:
Journal Article
Citation:
Statistics and Computing, 2017, 27 (3), pp. 833 - 844
Issue Date:
2017
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© 2016 Springer Science+Business Media New YorkThe widely applicable Bayesian information criterion (WBIC) is a simple and fast approximation to the model evidence that has received little practical consideration. WBIC uses the fact that the log evidence can be written as an expectation, with respect to a powered posterior proportional to the likelihood raised to a power (Formula presented.), of the log deviance. Finding this temperature value (Formula presented.) is generally an intractable problem. We find that for a particular tractable statistical model that the mean squared error of an optimally-tuned version of WBIC with correct temperature (Formula presented.) is lower than an optimally-tuned version of thermodynamic integration (power posteriors). However in practice WBIC uses the a canonical choice of (Formula presented.). Here we investigate the performance of WBIC in practice, for a range of statistical models, both regular models and singular models such as latent variable models or those with a hierarchical structure for which BIC cannot provide an adequate solution. Our findings are that, generally WBIC performs adequately when one uses informative priors, but it can systematically overestimate the evidence, particularly for small sample sizes.
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