Estimating Haplotype Structure and Frequencies: A Bayesian Approach to Unknown Design in Pooled Genomic Data

The estimation of haplotype structure and frequencies provides crucial information about the composition of genomes. Techniques, such as single-individual haplotyping, aim to reconstruct individual haplotypes from diploid genome sequencing data. However, our focus is distinct. We address the challenge of reconstructing haplotype structure and frequencies from pooled sequencing samples where multiple individuals are sequenced simultaneously. A frequentist method to address this issue has recently been proposed. In contrast to this and other methods that compute point estimates, our proposed Bayesian hierarchical model delivers a posterior that permits us to also quantify uncertainty. Since matching permutations in both haplotype structure and corresponding frequency matrix lead to the same reconstruction of their product, we introduce an order-preserving shrinkage prior that ensures identifiability with respect to permutations. For inference, we introduce a blocked Gibbs sampler that enforces the required constraints. In a simulation study, we assessed the performance of our method. Furthermore, by using our approach on two distinct sets of real data, we demonstrate that our Bayesian approach can reconstruct the dominant haplotypes in a challenging, high-dimensional set-up.