Data from: Probabilistic graphical model representation in phylogenetics

Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to statistical model representation and software development. Clear communication and representation of the chosen model is crucial for: (1) reproducibility of an analysis, (2) model development and (3) software design. Moreover, a unified, clear and understandable framework for model representation lowers the barrier for beginners and non-specialists to grasp complex phylogenetic models, including their assumptions and parameter/variable dependencies. Graphical modeling is a unifying framework that has gained in popularity in the statistical literature in recent years. The core idea is to break complex models into conditionally independent distributions. The strength lies in the comprehensibility, flexibility, and adaptability of this formalism, and the large body of computational work based on it. Graphical models are well-suited to teach statistical models, to facilitate communication among phylogeneticists and in the development of generic software for simulation and statistical inference. Here, we provide an introduction to graphical models for phylogeneticists and extend the standard graphical model representation to the realm of phylogenetics. We introduce a new graphical model component, tree plates, to capture the changing structure of the subgraph corresponding to a phylogenetic tree. We describe a range of phylogenetic models using the graphical model framework and introduce modules to simplify the representation of standard components in large and complex models. Phylogenetic model graphs can be readily used in simulation, maximum likelihood inference, and Bayesian inference using, for example, Metropolis-Hastings or Gibbs sampling of the posterior distribution.近年来，统计系统发育学（statistical phylogenetics）中所探索的模型空间快速扩张，凸显了对统计模型表示与软件开发新方法的迫切需求。清晰传达与呈现所选用的模型，对于以下三方面至关重要：(1) 分析结果的可重复性，(2) 模型开发，(3) 软件设计。此外，统一、清晰且易于理解的模型表示框架，能够降低初学者与非专业人员理解复杂系统发育模型的门槛，包括其假设前提与参数/变量依赖关系。图形建模（graphical modeling）是近年来统计学界日渐流行的统一框架，其核心思路是将复杂模型拆解为条件独立分布。该形式化方法的优势在于其优异的可理解性、灵活性与适配性，且已有大量基于该框架的计算研究成果。图形模型（graphical models）十分适用于统计模型的教学、助力系统发育学者间的学术交流，以及开发用于模拟与统计推断的通用软件。本文面向系统发育学者介绍图形模型，并将标准图形模型表示方法拓展至系统发育学领域。我们引入了一种全新的图形模型组件——树板（tree plates），用以刻画与系统发育树对应的子图的变化结构。我们借助图形模型框架描述了一系列系统发育模型，并引入模块化组件以简化大型复杂模型中标准组件的表示形式。系统发育模型图可便捷地应用于模拟、最大似然推断（maximum likelihood inference），以及基于后验分布的马尔可夫-黑斯廷斯（Metropolis-Hastings）采样或吉布斯（Gibbs）采样的贝叶斯推断（Bayesian inference）。