A nonparametric HMM for genetic imputation and coalescent inference

TL;DR

This paper introduces a nonparametric hidden Markov model based on the hierarchical Dirichlet process for genetic imputation and coalescent inference, offering a more flexible and parsimonious approach than existing models.

Contribution

It develops a truncation-free Bayesian nonparametric HMM with a new auxiliary sampling scheme, improving modeling of genetic data with nonhomogeneity and self transitions.

Findings

Outperforms the finite model fastPHASE in experiments.

Number of states correlates with the time to the most recent common ancestor.

Demonstrates flexibility of Bayesian nonparametrics for complex genetic data.

Abstract

Genetic sequence data are well described by hidden Markov models (HMMs) in which latent states correspond to clusters of similar mutation patterns. Theory from statistical genetics suggests that these HMMs are nonhomogeneous (their transition probabilities vary along the chromosome) and have large support for self transitions. We develop a new nonparametric model of genetic sequence data, based on the hierarchical Dirichlet process, which supports these self transitions and nonhomogeneity. Our model provides a parameterization of the genetic process that is more parsimonious than other more general nonparametric models which have previously been applied to population genetics. We provide truncation-free MCMC inference for our model using a new auxiliary sampling scheme for Bayesian nonparametric HMMs. In a series of experiments on male X chromosome data from the Thousand Genomes Project and also on data simulated from a population bottleneck we show the benefits of our model over the popular finite model fastPHASE, which can itself be seen as a parametric truncation of our model. We find that the number of HMM states found by our model is correlated with the time to the most recent common ancestor in population bottlenecks. This work demonstrates the flexibility of Bayesian nonparametrics applied to large and complex genetic data.