Laplace Approximations for Posterior Expectations When the Mode Occurs at the Boundary of the Parameter Space
本文针对众数在参数空间边界的情况，基于散度定理将高维积分转化为边界上的面积分，再用拉普拉斯方法得到二阶精度的后验期望近似，适用于两样本二项分布和随机效应模型。
Abstract This article gives asymptotic expansions for posterior expectations when the mode is on the boundary of the parameter space. The idea, based on the divergence theorem, is to reduce the high-dimensional integrals over the parameters space to surface integrals over the boundary of the parameter space and then apply the usual interior-mode Laplace method to the latter integrals. It is shown that these approximations have second-order accuracy. The method is illustrated with applications to a two-sample binomial problem and a random-eflects model.