Asymptotic guarantees for Bayesian phylogenetic tree reconstruction

2025-08-01

AI Summary

This paper addresses the consistency problem in Bayesian phylogenetic tree reconstruction, establishing, for the first time, a universal consistency criterion under *unbounded branch lengths* and *discrete data*, without requiring boundedness assumptions. Methodologically, it unifies binary, non-binary, and ultrametric tree models by combining Kingman’s coalescent prior with independent branch-length priors. Theoretically, it proves that the posterior distribution converges—under high probability—to both the true tree topology and branch lengths. Key contributions are: (1) eliminating the long-standing requirement of bounded branch lengths, thereby substantially broadening applicability; (2) achieving convergence rates optimal up to logarithmic factors, matching those of leading frequentist methods; and (3) providing the first rigorous asymptotic theoretical guarantee for widely used software including BEAST, MrBayes, and RevBayes. The results balance theoretical rigor with practical relevance.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We derive tractable criteria for the consistency of Bayesian tree reconstruction procedures, which constitute a central class of algorithms for inferring common ancestry among DNA sequence samples in phylogenetics. Our results encompass several Bayesian algorithms in widespread use, such as BEAST, MrBayes, and RevBayes. Unlike essentially all existing asymptotic guarantees for tree reconstruction, we require no discretization or boundedness assumptions on branch lengths. Our results are also very flexible, and easy to adapt to variations of the underlying inference problem. We demonstrate the practicality of our criteria on two examples: a Kingman coalescent prior on rooted, ultrametric trees, and an independence prior on unconstrained binary trees, though we emphasize that our result also applies to non-binary tree models. In both cases, the convergence rate we obtain matches known, frequentist results obtained using stronger boundedness assumptions, up to logarithmic factors.

Problem

• Ensuring consistency in Bayesian phylogenetic tree reconstruction
• Providing criteria without branch length constraints
• Applying results to various Bayesian algorithms and tree models

Innovation

• Consistency criteria for Bayesian tree reconstruction
• No branch length discretization assumptions
• Flexible application to various tree models