The Behavior of Metropolis-Coupled Markov Chains When Sampling Rugged Phylogenetic Distributions
The Behavior of Metropolis-Coupled Markov Chains When Sampling Rugged Phylogenetic Distributions
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DOI：
10.1093/sysbio/syy008
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发表时间：
2018-07-01
影响因子：
6.5
通讯作者：
Thomson, Robert C.
中科院分区：
文献类型：
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作者：
Brown, Jeremy M.;Thomson, Robert C.
贝叶斯系统发育推理依赖于使用马尔可夫链蒙特卡罗（MCMC）来提供高维积分的数值近似和估计后验概率。然而，当后验非常粗糙时（即，高后验密度区域被低后验密度区域分开），MCMC表现不佳。当分布不稳定时，用于改进MCMC数值估计的一种流行技术是Metropolis耦合（MC3）。在mc3中，额外的链用于采样后向的平坦化变换，并改善混合。在这里，我们强调了MC3的几个未被充分认识的行为。值得注意的是，当单个链不能很好地混合时，尽管不同的链从树空间的所有相关区域采样树，估计的后验概率可能是不正确的，但似乎是收敛的。与直觉相反的是，随着链条数量的增加，这种行为可能更难诊断。我们用一个简单的、非系统发育的例子和系统发育的例子来说明MC3的这些令人惊讶的行为，这些例子包括约束和非约束分析。为了检测和减轻这些行为的影响，我们建议增加独立分析的数量，并在当前版本的贝叶斯系统发育软件中改变最热链的温度。基于最热门链行为的聚合诊断也可以帮助检测这些行为，并可以在未来的软件版本中形成有用的补充。
Bayesian phylogenetic inference relies on the use of Markov chain Monte Carlo (MCMC) to provide numerical approximations of high-dimensional integrals and estimate posterior probabilities. However, MCMC performs poorly when posteriors are very rugged (i.e., regions of high posterior density are separated by regions of low posterior density). One technique that has become popular for improving numerical estimates from MCMC when distributions are rugged is Metropolis coupling (MC3). InMC3, additional chains are employed to sample flattened transformations of the posterior and improve mixing. Here, we highlight several underappreciated behaviors of MC3. Notably, estimated posterior probabilities may be incorrect but appear to converge, when individual chains do not mix well, despite different chains sampling trees from all relevant areas in tree space. Counterintuitively, such behavior can be more difficult to diagnose with increased numbers of chains. We illustrate these surprising behaviors of MC3 using a simple, non-phylogenetic example and phylogenetic examples involving both constrained and unconstrained analyses. To detect and mitigate the effects of these behaviors, we recommend increasing the number of independent analyses and varying the temperature of the hottest chain in current versions of Bayesian phylogenetic software. Convergence diagnostics based on the behavior of the hottest chain may also help detect these behaviors and could form a useful addition to future software releases.