论文标题
伯恩斯坦 - 冯·米塞斯定理和未指定的模型：评论
Bernstein - von Mises theorem and misspecified models: a review
论文作者
论文摘要
这是对模型规范下贝叶斯方法的渐近和非质合行为的综述。特别是，我们关注的是一致性，即以最佳参数近似为真模型的后验分布与点质量的收敛性，以及该点附近局部高斯的条件。对于指定的常规模型，高斯近似的方差与Fisher信息一致，从而使贝叶斯推断渐近地有效。在这篇综述中，我们讨论了这是如何受模型错误指定影响的。我们还讨论了调整贝叶斯推论的方法，以使其在模型错误指定下渐近效率。
This is a review of asymptotic and non-asymptotic behaviour of Bayesian methods under model specification. In particular we focus on consistency, i.e. convergence of the posterior distribution to the point mass at the best parametric approximation to the true model, and conditions for it to be locally Gaussian around this point. For well specified regular models, variance of the Gaussian approximation coincides with the Fisher information, making Bayesian inference asymptotically efficient. In this review, we discuss how this is affected by model misspecification. We also discuss approaches to adjust Bayesian inference to make it asymptotically efficient under model misspecification.
