Abstract: 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.
Key words and phrases: Bayesian nonparametric model, Dirichlet process, fixed effects, generalized linear mixed model, post-processing, random moments, random probability measure.