Hidden Markov Dirichlet Process: Modeling Genetic Recombination in Open Ancestral Space

We present a new statistical framework called hidden Markov Dirichlet process (HMDP) to jointly model the genetic recombinations among possibly infinite number of founders and the coalescence-with-mutation events in the resulting genealogies. The HMDP posits that a haplotype of genetic markers is generated by a sequence of recombination events that select an ancestor for each locus from an unbounded set of founders according to a 1st-order Markov transition process. Conjoining this process with a mutation model, our method accommodates both between-lineage recombination and withinlineage sequence variations, and leads to a compact and natural interpretation of the population structure and inheritance process. An efficient sampling algorithm based on a two-level nested Pólya urn scheme was also developed