Approximate Bayes Factors When a Mode Occurs on the Boundary
本文针对参数空间边界上出现后验众数的情况，提出边界众数拉普拉斯方法以近似贝叶斯因子，并修正了施瓦茨准则，同时探讨了嵌套模型检验中先验选择对贝叶斯因子的敏感性。
Bayes factors, measuring the strength of evidence in favor of the null, are often used in the Bayesian approach to testing hypotheses. Laplace approximations to Bayes factors are convenient and quite accurate in many contexts. However, one usual assumption—the existence of an interior mode—does not always hold. The posterior mode can occur at the boundary of the parameter space. This article discusses the boundary mode Laplace's method for boundary modes, uses it to approximate the Bayes factor, and presents a modification to the Schwarz criterion. The sensitivity of Bayes factor to the choice of prior on the nuisance parameter in testing nested models is also investigated. Results are illustrated for the case of testing extrabinomial variability.