For predictive evaluation based on quasi-posterior distributions, we develop a new information criterion, the posterior covariance information criterion (PCIC. PCIC generalises the widely applicable information criterion WAIC so as to effectively handle predictive scenarios where likelihoods for the estimation and the evaluation of the model may be different. A typical example of such scenarios is the weighted likelihood inference, including prediction under covariate shift and counterfactual prediction. The proposed criterion utilises a posterior covariance form and is computed by using only one Markov chain Monte Carlo run. Through numerical examples, we demonstrate how PCIC can apply in practice. Further, we show that PCIC is asymptotically unbiased to the quasi-Bayesian generalization error under mild conditions in weighted inference with both regular and singular statistical models.
翻译:对于基于准内存分布的预测性评价,我们制定了一个新的信息标准,即后置信息标准(PCIC. PCIC. PCIC. 将广泛适用的信息标准概括为WAIC, 以便有效地处理预测性情景,其中估计和评价模型的可能性可能不同。这种情景的一个典型例子是加权可能性推理,包括在共变转移和反事实预测下的预测。拟议标准使用后置变量形式,仅使用一个Markov链 Monte Carlo 运行计算。我们通过数字实例,展示PCIC如何在实践中应用。此外,我们表明,PCIC在与常规和单一统计模型加权推论的轻度条件下,对准Bayesian一般化错误是无偏见的。