Posterior bimodality in the balanced one-way random-effects model

Jiannong Liu, James S. Hodges

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Although some researchers have examined posterior multimodality for specific richly parameterized models, multimodality is not well characterized for any such model. The paper characterizes bimodality of the joint and marginal posteriors for a conjugate analysis of the balanced one-way random-effects model with a flat prior on the mean. This apparently simple model has surprisingly complex and even bizarre mode behaviour. Bimodality usually arises when the data indicate a much larger between-groups variance than does the prior. We examine an example in detail, present a graphical display for describing bimodality and use real data sets from a statistical practice to shed light on the practical relevance of bimodality for these models.

Original languageEnglish (US)
Pages (from-to)247-255
Number of pages9
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number1
StatePublished - 2003


  • Bayesian analysis
  • Bimodality
  • Hierarchical model
  • Prior distribution
  • Random effects
  • Variance components

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