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Center-adjusted inference for a nonparametric Bayesian random effect distribution. (English) Zbl 1223.62079

Summary: 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 data set. 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.

MSC:

62G99 Nonparametric inference
62F15 Bayesian inference
65C60 Computational problems in statistics (MSC2010)
62J12 Generalized linear models (logistic models)
65C40 Numerical analysis or methods applied to Markov chains
62P10 Applications of statistics to biology and medical sciences; meta analysis
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