Model misspecification, Bayesian versus credibility estimation, and Gibbs posteriors
Model misspecification, Bayesian versus credibility estimation, and Gibbs posteriors
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DOI：
10.1080/03461238.2019.1711154
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发表时间：
2020-01-14
影响因子：
1.8
通讯作者：
Martin, Ryan
中科院分区：
文献类型：
--
作者：
Hong, Liang;Martin, Ryan
在预测未来索赔的背景下，完全贝叶斯分析（指定统计模型、先验分布并使用贝叶斯公式进行更新的分析）通常被视为黄金标准，而布尔曼的可信度估计量则充当简单的近似值。但是，那些赋予贝叶斯解决方案较高地位的理想属性关键取决于正确指定的假设模型。在这里，我们研究了错误指定模型下贝叶斯后验分布的渐近行为，我们的结论是错误指定偏差通常会产生破坏性影响，可能导致不准确的推理和预测。另一方面，可信度估计器对模型错误指定完全不敏感，这使得它在模型不确定的实际相关情况下比贝叶斯解决方案更具优势。这就引出了一个问题：模型错误指定的稳健性是否要求我们放弃基于后验分布的不确定性量化？我们对这个问题的回答是否定的，我们提供了另一种吉布斯后验结构。此外，我们认为吉布斯的观点提供了布尔曼可信度估计量的新特征。
In the context of predicting future claims, a fully Bayesian analysis - one that specifies a statistical model, prior distribution, and updates using Bayes's formula - is often viewed as the gold-standard, while Buhlmann's credibility estimator serves as a simple approximation. But those desirable properties that give the Bayesian solution its elevated status depend critically on the posited model being correctly specified. Here we investigate the asymptotic behavior of Bayesian posterior distributions under a misspecified model, and our conclusion is that misspecification bias generally has damaging effects that can lead to inaccurate inference and prediction. The credibility estimator, on the other hand, is not sensitive at all to model misspecification, giving it an advantage over the Bayesian solution in those practically relevant cases where the model is uncertain. This begs the question: does robustness to model misspecification require that we abandon uncertainty quantification based on a posterior distribution? Our answer to this question is No, and we offer an alternative Gibbs posterior construction. Furthermore, we argue that this Gibbs perspective provides a new characterization of Buhlmann's credibility estimator.