Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by modeling the large number of unknown parameters as random effects from a common prior distribution. However, misspecification of the prior distribution can lead to erroneous estimates of the random effects, especially for the largest and most interesting effects. This article has two aims. First, we propose a robustified posterior distribution for a parametric Bayesian hierarchical model that can substantially reduce the impact of a misspecified prior. Second, we conduct a systematic comparison of the standard parametric posterior, the proposed robustified parametric posterior, and nonparametric Bayesian posterior which uses a Dirichlet process mixture prior. The proposed robustified posterior when combined with a flexible parametric prior can be a superior alternative to nonparametric Bayesian methods.

Original languageEnglish (US)
Pages (from-to)145-151
Number of pages7
JournalAmerican Statistician
Issue number2
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'A Robustified Posterior for Bayesian Inference on a Large Number of Parallel Effects'. Together they form a unique fingerprint.

Cite this