Comparison of Bayesian and maximum-likelihood inference of population genetic parameters

TLDR

Comparing performance and accuracy of ML and Bayesian inference is challenging because they are implemented in different programs, and the ML framework can fail on sparse data and produce non‑conservative support intervals. The study aims to show that a Bayesian framework with suitable priors can address the shortcomings of the ML approach. Both methods are implemented in the MIGRATE program, which uses a shared MCMC algorithm but differs in proposal distribution and likelihood maximization, allowing direct comparison under identical population models. Simulations show that the Bayesian method generally outperforms ML in accuracy and coverage, though they are comparable for some parameter values, and MIGRATE was extended to support both inference modes. The MIGRATE program, available via contact at [e-mail], supports both inference approaches.

Abstract

Abstract Comparison of the performance and accuracy of different inference methods, such as maximum likelihood (ML) and Bayesian inference, is difficult because the inference methods are implemented in different programs, often written by different authors. Both methods were implemented in the program MIGRATE, that estimates population genetic parameters, such as population sizes and migration rates, using coalescence theory. Both inference methods use the same Markov chain Monte Carlo algorithm and differ from each other in only two aspects: parameter proposal distribution and maximization of the likelihood function. Using simulated datasets, the Bayesian method generally fares better than the ML approach in accuracy and coverage, although for some values the two approaches are equal in performance. Motivation: The Markov chain Monte Carlo-based ML framework can fail on sparse data and can deliver non-conservative support intervals. A Bayesian framework with appropriate prior distribution is able to remedy some of these problems. Results: The program MIGRATE was extended to allow not only for ML(-) maximum likelihood estimation of population genetics parameters but also for using a Bayesian framework. Comparisons between the Bayesian approach and the ML approach are facilitated because both modes estimate the same parameters under the same population model and assumptions. Availability: The program is available from Contact: [e-mail]