# Bayes estimators for phylogenetic reconstruction

## TL;DR

This paper introduces a Bayesian approach to phylogenetic tree reconstruction by proposing the Bayes estimator, which maximizes expected accuracy and outperforms traditional methods like ML and neighbor joining in simulated data.

## Contribution

The paper develops a unified framework for Bayes estimators in phylogenetics, especially for tree distances like Robinson--Foulds, and demonstrates their practical computation and improved accuracy.

## Key findings

- Bayes estimators can be efficiently computed via hill climbing.
- Bayes estimators outperform ML and neighbor joining in accuracy.
- The framework applies to various tree distance measures.

## Abstract

Tree reconstruction methods are often judged by their accuracy, measured by how close they get to the true tree. Yet most reconstruction methods like ML do not explicitly maximize this accuracy. To address this problem, we propose a Bayesian solution. Given tree samples, we propose finding the tree estimate which is closest on average to the samples. This ``median'' tree is known as the Bayes estimator (BE). The BE literally maximizes posterior expected accuracy, measured in terms of closeness (distance) to the true tree. We discuss a unified framework of BE trees, focusing especially on tree distances which are expressible as squared euclidean distances. Notable examples include Robinson--Foulds distance, quartet distance, and squared path difference. Using simulated data, we show Bayes estimators can be efficiently computed in practice by hill climbing. We also show that Bayes estimators achieve higher accuracy, compared to maximum likelihood and neighbor joining.