Multimodality is common in many scientific and engineering applications. However, standard Markov chain Monte Carlo (MCMC) convergence diagnostics often penalise multimodality in practice by conflating overall poor mixing with groups of chains that have mixed well within distinct modes. To diagnose multimodality rather than flag it as a sampling failure, we introduce the MCMC convergence graph: a graph-based diagnostic that computes pairwise R-hat values between chains and summarises them in a graph, revealing sets of chains that explore the same posterior mode. We implement the method in the probabilistic programming framework Stan and demonstrate its use on worked examples ranging from regression models with inherent multimodality in the data, to a pharmacokinetic model for which multimodality reflects non-identifiability. The graph-based diagnostic, which we make freely available in the R package mcmcConvergenceGraph and which accepts MCMC output from any sampler, provides both graphical and numerical summaries of MCMC behaviour for diagnosing multimodality.

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