35
views
0
recommends
+1 Recommend
0 collections
    4
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Investigation of the widely applicable Bayesian information criterion

      Preprint
      , , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          The 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 \(t^*\in{(0,1)}\), of the log deviance. Finding this temperature value \(t^*\) 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 \(t^*\) is lower than an optimally-tuned version of thermodynamic integration (power posteriors). However in practice WBIC uses the a canonical choice of \(t=1/\log(n)\). 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.

          Related collections

          Author and article information

          Journal
          2015-01-22
          2016-04-28
          Article
          1501.05447
          5fadbf54-a1f9-4995-8521-95d65f727031

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          To appear in Statistics and Computing
          stat.ME

          Methodology
          Methodology

          Comments

          Comment on this article