Abstract

A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated parameter values for corresponding posterior distributions are uniformly distributed. Checking for uniformity when a posterior density is approximated numerically provides a diagnostic for algorithm validity. Furthermore, adjustments to achieve uniformity can improve the quality of approximate inference methods. The present article develops a moment-based alternative to the conventional checking and adjustment methods using quantiles. The new approach relates prior and posterior expectations and covariances through the tower property of conditional expectation and the law of total variance. For adjustment, approximate inferences are modified so that the correct prior to posterior relationships hold. We illustrate the method in three examples. The first uses an auxiliary model in a likelihood-free inference problem. The second considers corrections for variational Bayes approximations in a deep neural network generalized linear mixed model. Our final application considers a deep neural network surrogate for approximating Gaussian process regression predictive inference. Supplementary files for this article are available online.

摘要

评估贝叶斯抽样或近似推理方法有效性的常用方法是利用模拟数据复制来获取从先验得出的参数。在连续性假设下，对应后验分布的模拟参数值的函数分位数是均匀分布的。在数值近似后验密度时检查均匀性提供了算法有效性的诊断。此外，为实现一致性而进行的调整可以提高近似推理方法的质量。本文开发了一种基于矩的替代方法，以替代使用分位数的传统检查和调整方法。新方法通过条件期望的塔性质和总方差定律将先验和后验期望以及协方差联系起来。为了调整，近似推论被修改，以便正确的先验关系成立。我们用三个例子来说明这个方法。第一个在无似然推理问题中使用辅助模型。第二个考虑修正深度神经网络广义线性混合模型中的变分贝叶斯近似。我们的最终应用考虑了用于近似高斯过程回归预测推理的深度神经网络代理。本文的补充文件可在线获取。第二个考虑修正深度神经网络广义线性混合模型中的变分贝叶斯近似。我们的最终应用考虑了用于近似高斯过程回归预测推理的深度神经网络代理。本文的补充文件可在线获取。第二个考虑修正深度神经网络广义线性混合模型中的变分贝叶斯近似。我们的最终应用考虑了用于近似高斯过程回归预测推理的深度神经网络代理。本文的补充文件可在线获取。