Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has several optimal properties, a major drawback of Bayesian inference is the lack of robustness against data contamination and model misspecification, which becomes pernicious in the use of objective priors. This paper presents the general formulation of a Bayes pseudo-posterior distribution yielding robust inference. Exponential convergence results related to the new pseudo-posterior and the corresponding Bayes estimators are established under the general parametric set-up and illustrations are provided for the independent stationary as well as non-homogeneous models. Several additional details and properties of the procedure are described, including the estimation under fixed-design regression models.

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一般稳健贝叶斯伪后验：指数收敛结果与应用

尽管贝叶斯推理是包括统计学家在内的一大批科学家中非常流行的范式，但大多数应用程序都考虑了客观先验并需要进行批判性调查（Efron，2013，Science）。虽然它有几个最佳属性，但贝叶斯推理的一个主要缺点是缺乏对数据污染和模型错误指定的鲁棒性，这在使用客观先验时变得有害。本文介绍了产生稳健推理的贝叶斯伪后验分布的一般公式。在一般参数设置下建立了与新伪后验和相应贝叶斯估计量相关的指数收敛结果，并为独立平稳和非齐次模型提供了说明。