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Posterior bimodality in the balanced one-way random-effects model
Authors:Jiannong Liu  James S Hodges
Institution:Minneapolis Medical Research Foundation, USA; University of Minnesota, Minneapolis, USA
Abstract:Summary. 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.
Keywords:Bayesian analysis  Bimodality  Hierarchical model  Prior distribution  Random effects  Variance components
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