Abstract For existing Bayesian cross-validated measure of influence of each observation on the posterior distribution, this paper considers a generalization using the Bregman Divergence (BD). We investigate various practically useful and desirable properties of these BD based measures to demonstrate the superiority of these measures compared to existing Bayesian measures of influence and Bayesian residual based diagnostics. We provide a practical and easily comprehensible method for calibrating these BD based measures. Also, we show how to compute our BD based measure via Monte Carlo Markov Chain (MCMC) samples from a single posterior based on the full data. Using a Bayesian meta-analysis of clinical trials, we illustrate how our new measures of influence of observations have more useful practical roles for data analysis than popular Bayesian residual analysis tools.

中文翻译：

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Bregman divergence 泛化贝叶斯影响度量以进行数据分析

摘要 对于现有的贝叶斯交叉验证测量每个观测值对后验分布的影响，本文考虑使用 Bregman Divergence (BD) 进行泛化。我们研究了这些基于 BD 的度量的各种实际有用和理想的特性，以证明这些度量与现有的贝叶斯影响度量和基于贝叶斯残差的诊断相比的优越性。我们提供了一种实用且易于理解的方法来校准这些基于 BD 的措施。此外，我们展示了如何通过基于完整数据的单个后验样本的蒙特卡罗马尔可夫链 (MCMC) 样本计算基于 BD 的度量。使用贝叶斯荟萃分析临床试验，