6533b825fe1ef96bd12833f4
RESEARCH PRODUCT
Prior-based Bayesian information criterion
James O. BergerLuis R. PericchiMaria J. BayarriIngmar VisserWoncheol JangSurajit Raysubject
Statistics and ProbabilityLaplace expansionApplied MathematicsBayes factorMarginal likelihoodStatistics::Computationsymbols.namesakeComputational Theory and MathematicsLaplace's methodBayesian information criterionPrior probabilitysymbolsApplied mathematicsStatistics::MethodologyStatistics Probability and UncertaintyLikelihood functionFisher informationAnalysisMathematicsdescription
We present a new approach to model selection and Bayes factor determination, based on Laplace expansions (as in BIC), which we call Prior-based Bayes Information Criterion (PBIC). In this approach, the Laplace expansion is only done with the likelihood function, and then a suitable prior distribution is chosen to allow exact computation of the (approximate) marginal likelihood arising from the Laplace approximation and the prior. The result is a closed-form expression similar to BIC, but now involves a term arising from the prior distribution (which BIC ignores) and also incorporates the idea that different parameters can have different effective sample sizes (whereas BIC only allows one overall sample size n). We also consider a modification of PBIC which is more favourable to complex models.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-01-01 |