改进在多物种溯祖模型下用于系统发育推断的贝叶斯MCMC算法的混合效率

在多物种溯祖(MSC)模型下利用DNA序列数据进行系统发育推断是物种进化研究的基础。相应的推断方法中，贝叶斯框架下的MCMC方法比启发式方法统计性质好，比ML方法可行性强。但当数据量较大时，MCMC算法面临效率低下，计算耗时的问题。因此，改进MCMC算法的效率是在基因组大数据时代准确有效地进行系统发育推断的关键。本项目旨在改进MSC框架下用于系统发育推断的贝叶斯MCMC算法的混合效率，减少算法收敛所需迭代次数，提高其处理大数据的能力。同时期望以此为契机，建立一般性改进MCMC混合效率的统计学理论。用于系统发育推断的MCMC算法包含模型内和模型间两类。本项目将用理论推导结合数据分析，从提议分布的选择出发，针对这两类MCMC分别改进。另外，本项目将通过仿真实验探索在不同系统发育模型和基因序列数据设置下，Metropolis-coupled MCMC算法改进效率的表现，为实践选择提供指导。

Phylogenetic inference using DNA sequence data under the multispecies coalescent (MSC) model is fundamental for the research of species evolution. Among the various inference methods, Bayesian MCMC has better statistical properties than heuristic methods and is more feasible than the ML method. However, when the data size is large, the MCMC algorithms will suffer from poor efficiency and become computationally time-consuming. As a result, improving the efficiency of MCMC is crucial for making accurate and effective phylogenetic inference in the era of genome-scale data. This project aims at improving the mixing efficiency of the MCMC algorithms used for phylogenetic inference under the MSC framework, reducing the numbers of iterations that the algorithms require to reach convergence, and then enhancing their capacity to address big data. Also, we expect to use this application as the springboard to establish the general statistical theories for improving the mixing efficiency of MCMC. The Bayesian MCMC algorithm for phylogenetic inference includes two types of moves, within-model moves and cross-model moves. Therefore, the project will improve the mixing efficiency of within-model MCMC and cross-model MCMC respectively by combining theoretical arguments with data analysis and focusing on how to choose the proposal distributions. On the other hand, this project will use simulation studies to investigate the performance of the Metropolis-coupled MCMC algorithm on improving mixing efficiency under different settings of phylogenetic inference models and genetic sequence data, with the expectation to provide instructions on when to use this algorithm in practice.