We establish a connection between Bayesian case influence measures for assessing the influence of individual observations and Bayesian predictive methods for evaluating the predictive performance of a model and comparing different models fitted to the same dataset. Based on such a connection, we formally propose a new set of Bayesian case-deletion model complexity (BCMC) measures for quantifying the effective number of parameters in a given statistical model. Its properties in linear models are explored. Adding some functions of BCMC to a conditional deviance function leads to a Bayesian case-deletion information criterion (BCIC) for comparing models. We systematically investigate some properties of BCIC and its connection with other information criteria, such as the Deviance Information Criterion (DIC). We illustrate the proposed methodology on linear mixed models with simulations and a real data example.

中文翻译：

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贝叶斯案例删除模型复杂性和信息标准

我们在用于评估个体观察影响的贝叶斯案例影响度量与用于评估模型预测性能和比较适合同一数据集的不同模型的贝叶斯预测方法之间建立联系。基于这种联系，我们正式提出了一组新的贝叶斯案例删除模型复杂度 (BCMC) 度量，用于量化给定统计模型中的有效参数数量。探索了它在线性模型中的特性。将 BCMC 的一些函数添加到条件偏差函数会导致用于比较模型的贝叶斯案例删除信息标准 (BCIC)。我们系统地研究了 BCIC 的一些属性及其与其他信息标准的联系，例如偏差信息标准 (DIC)。