Risk of Bayesian Inference in Misspecified Models, and the Sandwich Covariance Matrix
研究了在误设定的参数模型中，贝叶斯后验分布与极大似然估计的渐近方差不同，导致贝叶斯推断的风险较高，并提出了用三明治协方差矩阵构造人工正态后验来降低风险的算法。
It is well known that, in misspecified parametric models, the maximum likelihood estimator (MLE) is consistent for the pseudo-true value and has an asymptotically normal sampling distribution with "sandwich" covariance matrix. Also, posteriors are asymptotically centered at the MLE, normal, and of asymptotic variance that is, in general, different than the sandwich matrix. It is shown that due to this discrepancy, Bayesian inference about the pseudo-true parameter value is, in general, of lower asymptotic frequentist risk when the original posterior is substituted by an artificial normal posterior centered at the MLE with sandwich covariance matrix. An algorithm is suggested that allows the implementation of this artificial posterior also in models with high dimensional nuisance parameters which cannot reasonably be estimated by maximizing the likelihood.