A nonparametric HMM for genetic imputation and coalescent inference
This work addresses genetic imputation and coalescent inference for population genetics, offering a more parsimonious model but is incremental as it builds on existing nonparametric methods.
The authors tackled the problem of modeling genetic sequence data with hidden Markov models (HMMs) that are nonhomogeneous and support self-transitions, developing a nonparametric model based on the hierarchical Dirichlet process. They demonstrated its benefits over the finite model fastPHASE on real and simulated data, showing correlation between HMM states and time to the most recent common ancestor in population bottlenecks.
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.