Dirichlet process (DP) priors are a popular choice for semiparametric Bayesian random effect models. The fact that the DP prior implies a non-zero mean for the random effect distribution creates an identifiability problem that complicates the interpretation of, and inference for, the fixed effects that are paired with the random effects. Similarly, the interpretation of, and inference for, the variance components of the random effects also becomes a challenge. We propose an adjustment of conventional inference using a post-processing technique based on an analytic evaluation of the moments of the random moments of the DP. The adjustment for the moments of the DP can be conveniently incorporated into Markov chain Monte Carlo simulations at essentially no additional computational cost. We conduct simulation studies to evaluate the performance of the proposed inference procedure in both a linear mixed model and a logistic linear mixed effect model. We illustrate the method by applying it to a prostate specific antigen dataset. We provide an R function that allows one to implement the proposed adjustment in a post-processing step of posterior simulation output, without any change to the posterior simulation itself.

中文翻译：

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非参数贝叶斯随机效应分布的中心调整推理

Dirichlet 过程 (DP) 先验是半参数贝叶斯随机效应模型的流行选择。DP 先验意味着随机效应分布的非零均值这一事实产生了可识别性问题，这使得与随机效应配对的固定效应的解释和推断复杂化。同样，对随机效应的方差分量的解释和推断也成为一个挑战。我们建议使用基于对 DP 的随机矩的矩的分析评估的后处理技术对常规推理进行调整。DP 矩的调整可以方便地合并到马尔可夫链蒙特卡洛模拟中，基本上没有额外的计算成本。我们进行模拟研究以评估所提出的推理过程在线性混合模型和逻辑线性混合效应模型中的性能。我们通过将其应用于前列腺特异性抗原数据集来说明该方法。我们提供了一个 R 函数，它允许人们在后验模拟输出的后处理步骤中实施建议的调整，而无需对后验模拟本身进行任何更改。