发表机构
Uppsala University; Chalmers University of Technology; University of Gothenburg（乌普萨拉大学; 查尔姆斯理工大学; 哥德堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对标准MCMC诊断误判多峰后验的问题，提出基于图的MCMC收敛图诊断方法，通过成对R-hat值识别同峰链组，在Stan中实现并提供R包。
AI 中文摘要
多峰性在许多科学和工程应用中很常见。然而，标准的马尔可夫链蒙特卡罗（MCMC）收敛诊断在实践中常常通过将整体混合不良与已在不同峰内良好混合的链组混为一谈，从而对多峰性进行惩罚。为了诊断多峰性而非将其标记为采样失败，我们引入了MCMC收敛图：一种基于图的诊断方法，计算链之间的成对R-hat值，并将其汇总成图，揭示探索同一后验峰的链组。我们在概率编程框架Stan中实现了该方法，并在从数据中具有固有多峰性的回归模型到多峰性反映不可辨识性的药代动力学模型等实例中展示了其用途。这种基于图的诊断方法，我们在R包mcmcConvergenceGraph中免费提供，并接受来自任何采样器的MCMC输出，为诊断多峰性提供MCMC行为的图形和数值摘要。
英文摘要
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.
Comments16 pages (main manuscript) + 2 pages (appendix); 6 figures (main manuscript) + 2 figures (appendix); 3 tables (main manuscript)
