Markov Chains on Phylogenetic Tree Spaces

系统发生树是生物学中进化过程的基本数学表示。它们的特点是与“大数据”相关的挑战，以及它们的离散几何结构导致非欧几里得树空间的复杂性，造成了重大的计算和统计限制。纯数学的一个理论结果建立了一个代数几何树空间，它最近被证明支持严格的统计和概率研究。本项目将通过利用代数几何树空间的结构和组合特性来表征其信息几何形状，并将马尔可夫链用于统计推断，从而实际实施此类研究。

Phylogenetic trees are the fundamental mathematical representation ofevolutionary processes in biology. They are characterized by thechallenges associated with "big data," as well as the complication thattheir discrete geometric structure results in a non-Euclidean tree space,posing significant computational and statistical limitations. A theoreticalresult from pure mathematics establishes an algebraic geometric treespace, which has recently been shown to support rigorous statistical andprobabilistic studies. This project will practically implement such studiesby harnessing the structural and combinatorial properties of the algebraicgeometric tree space to characterize its information geometry and adaptMarkov chains for statistical inference.