Markov Genealogy Processes

TL;DR

This paper introduces a family of Markov processes for genealogies derived from population models, providing exact likelihood formulas and filtering methods to improve inference in evolutionary studies.

Contribution

It develops a new theoretical framework linking genealogy-valued Markov processes with population dynamics, enabling efficient inference algorithms.

Findings

Derived exact likelihood expressions for genealogies.

Formulated nonlinear filtering equations for inference.

Demonstrated methods with practical examples.

Abstract

We construct a family of genealogy-valued Markov processes that are induced by a continuous-time Markov population process. We derive exact expressions for the likelihood of a given genealogy conditional on the history of the underlying population process. These lead to a nonlinear filtering equation which can be used to design efficient Monte Carlo inference algorithms. We demonstrate these calculations with several examples. Existing full-information approaches for phylodynamic inference are special cases of the theory.