Identifiability of Large Phylogenetic Mixture Models

TL;DR

This paper investigates the identifiability of parameters in large phylogenetic mixture models, demonstrating that both numerical and tree parameters are identifiable when all trees are identical, and explores extensions to different trees.

Contribution

The paper provides new algebraic methods to establish parameter identifiability in large phylogenetic mixture models with multiple components.

Findings

Numerical and tree parameters are identifiable when all trees are the same.

Algebraic techniques can potentially extend identifiability results to mixtures on different trees.

The analysis applies to models with many mixture components on large trees.

Abstract

Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. The fundamental question of whether parameters of such a model are identifiable is difficult to address, due to the complexity of the parameterization. We analyze mixture models on large trees, with many mixture components, showing that both numerical and tree parameters are indeed identifiable in these models when all trees are the same. We also explore the extent to which our algebraic techniques can be employed to extend the result to mixtures on different trees.