We present a new approach to model selection and Bayes factor determination,based on Laplaceexpansions(as in BIC),which we call Prior-based Bayes Information Criterion(PBIC).In thisapproach,the Laplace expansion is on...We present a new approach to model selection and Bayes factor determination,based on Laplaceexpansions(as in BIC),which we call Prior-based Bayes Information Criterion(PBIC).In thisapproach,the Laplace expansion is only done with the likelihood function,and then a suitableprior distribution is chosen to allow exact computation of the(approximate)marginal likelihoodarising 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)andalso 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 whichis more favourable to complex models.展开更多
基金M.J.Bayarri’s research was supported by the Spanish Ministry of Education and Science[grant number MTM2010-19528]James Berger’s research was supported by USA National Science Foundation[grant numbers DMS-1007773 and DMS-1407775]+1 种基金Woncheol Jang’s research was supported by the National Research Foundation of Korea(NRF)grants funded by the Korea government(MSIP),No.2014R1A4A1007895 and No.2017R1A2B2012816Luis Pericchi’s research was supported by grant CA096297/CA096300 from the USA National Cancer Institute of the National Institutes of Health.
文摘We present a new approach to model selection and Bayes factor determination,based on Laplaceexpansions(as in BIC),which we call Prior-based Bayes Information Criterion(PBIC).In thisapproach,the Laplace expansion is only done with the likelihood function,and then a suitableprior distribution is chosen to allow exact computation of the(approximate)marginal likelihoodarising 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)andalso 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 whichis more favourable to complex models.
