DMS/NIGMS 2: Scalable Bayesian Inference with Applications to Phylogenetics

该项目涉及贝叶斯推理方法，这是科学方法的一种变体，用于量化特定假设的确定性程度。这项工作的动机是应用于系统发生分析方法，这有助于推断进化史，并促进了将现存和化石物种放在生命树上的重大进展。然而，由于性能的限制，现有的方法无法推断出完整的生命树。此外，当同一物种之间发生基因交换时，树的比喻就失效了，需要额外的联系来形成一个生命网络。该项目旨在开发改进的方法，不仅可以扩展到推断完整生命树的挑战，而且可以以一种原则性的方式确保能够量化估计树和网络的信心程度。这些改进有望应用于其他研究领域，远远超出系统发育和进化生物学。该项目还将为研究生提供培训和研究机会，并为教师提供研究经验。马尔可夫链蒙特卡罗（MCMC）算法广泛适用于贝叶斯推理，经常用于实现系统发育分析方法。该项目的总体目标是开发具有数学保证的贝叶斯MCMC推理的显著可扩展性的技术。虽然这项工作将在系统基因组学中实施和说明，但它适用于使用MCMC的所有领域。为了实现这一目标，该研究旨在在四个领域开发新的方法和数学结果：(1)利用现代多核和多核计算硬件进行并行计算的似然函数和计算；(2)对复杂图进行采样，以避免在系统发育树和网络空间中行走，避免离散和连续参数的混合以及可逆跳跃移动和Hastings比率计算的相关复杂性；(3)结构化先验分布，以改善混合；(4)基于现有技术和本项目开发的技术，采用分而治之的方法进行大规模推理。除了建立数学结果外，所有方法都将在模拟和观察的生物数据上进行彻底的实施和测试。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project concerns methods for Bayesian inference, a variation on the scientific method that quantifies the degree of certainty in a particular hypothesis. The work is motivated by application to phylogenic analysis methods, which help to infer evolutionary history and have facilitated great progress towards placing extant and fossil species on the tree of life. However, existing methods are unable to infer a complete tree of life due to performance limitations. Additionally, the metaphor of a tree breaks down when exchange of genes occurs between contemporaneous species, necessitating additional links to form a network of life. This project aims to develop improved methods that not only scale to the challenge of inferring a complete tree of life but do so in a principled way that ensures the ability to quantify degree of confidence in estimated trees and networks. These improvements are expected to be applicable to other areas of research as well, far beyond phylogenetics and evolutionary biology. This project will also provide training and research opportunities for graduate students and research experiences for teachers.The Markov-Chain Monte Carlo (MCMC) algorithm is broadly applicable for Bayesian inference and often used to implement phylogenetic analysis methods. The overarching goal of this project is to develop techniques for significant scalability of Bayesian MCMC inference with mathematical guarantees. While the work will be implemented for and illustrated in phylogenomics, it is applicable to all domains where MCMC is used. To achieve this, the research aims to develop novel methods and mathematical results in four areas: (1) likelihood functions and calculations for parallel computation to take advantage of modern multi- and many-core computing hardware, (2) sampling over complex graphs to avoid walking in the space of phylogenetic trees and networks with its mix of discrete and continuous parameters and associated complexity of reversible jump moves and Hastings ratio calculations, (3) structured prior distributions to improve mixing, and (4) a divide-and-conquer approach to large scale inference building on existing techniques and those developed in this project. In addition to establishing mathematical results, all methods will be implemented and tested thoroughly on simulated and observed biological data.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.