Bayesian inference is a popular and widely-used approach to infer phylogenies (evolutionary trees). However, despite decades of widespread application, it remains difficult to judge how well a given Bayesian Markov chain Monte Carlo (MCMC) run explores the space of phylogenetic trees. In this paper, we investigate the Monte Carlo error of phylogenies, focusing on high-dimensional summaries of the posterior distribution, including variability in estimated edge/branch (known in phylogenetics as "split") probabilities and tree probabilities, and variability in the estimated summary tree. Specifically, we ask if there is any measure of effective sample size (ESS) applicable to phylogenetic trees which is capable of capturing the Monte Carlo error of these three summary measures. We find that there are some ESS measures capable of capturing the error inherent in using MCMC samples to approximate the posterior distributions on phylogenies. We term these tree ESS measures, and identify a set of three which are useful in practice for assessing the Monte Carlo error. Lastly, we present visualization tools that can improve comparisons between multiple independent MCMC runs by accounting for the Monte Carlo error present in each chain. Our results indicate that common post-MCMC workflows are insufficient to capture the inherent Monte Carlo error of the tree, and highlight the need for both within-chain mixing and between-chain convergence assessments.
翻译:在本文中,我们调查了植物遗传树的蒙特卡洛(MCMC)对植物遗传树空间的探索能力。我们发现,在利用植物遗传分布的高维摘要中,有一些ESS措施能够捕捉到在利用MMC采集样本来估计植物遗传分布时所固有的错误。我们用这些树类ESS措施来说明这些树类ESS措施,并找出一套有助于评估MAC内部误差的三套做法。最后,我们用观察工具来说明目前MAC的多重误差。我们目前通过观察工具可以发现,MESS措施能够捕捉到利用MMC采集样本在植物分布上的误差。我们称之为树类ESS措施,并找出一套有助于评估MTC内部误差的三套做法。