## Detecting Poor Convergence of Posterior Samplers due to Multimodality

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### BibTeX

@MISC{Woodard_detectingpoor,

author = {Dawn B. Woodard},

title = {Detecting Poor Convergence of Posterior Samplers due to Multimodality},

year = {}

}

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### Abstract

Computation in Bayesian statistical models is often performed us-ing sampling techniques such as Markov chain Monte Carlo (MCMC) or adaptive Monte Carlo methods. The convergence of the sampler to the posterior distribution is typically assessed using a set of standard diag-nostics; recent draft Food and Drug Administration guidelines for the use of Bayesian statistics in medical device trials, for instance, advocate this approach for validating computations. We give several examples showing that this approach may be in-sufficient when the posterior distribution is multimodal–that lack of convergence due to posterior multimodality can be undetected using the standard convergence diagnostics, including the Gelman-Rubin di-agnostic that was introduced for exactly this problem. We show that the poor convergence can be detected by modifying a validation technique that was originally proposed for detecting coding errors in MCMC soft-