A0749
Title: Haplotype reconstruction via Bayesian linear models with unknown design
Authors: Yuexuan Wang - Johannes Kepler University Linz (Austria) [presenting]
Abstract: The topic is the reconstruction of the unknown matrices $S$ and $\omega$ for the multivariate linear model $Y = S\omega+\varepsilon$ under the assumption of binary entries $s_{ij}\in \{0,1\}$ for $S$ and $\omega$ is a weight matrix. While a frequentist method has recently been proposed for this purpose, a Bayesian approach also seems desirable. In contrast to the point estimates provided by this frequentist method, our proposed hierarchical model delivers a posterior that permits quantifying uncertainty. Since matching permutations in both $S$ and $\omega$ lead to the same reconstruction $S\omega$, an order-preserving shrinkage prior is introduced to establish identifiability concerning permutations. For inference, a blocked Metropolis-Hastings is introduced within the Gibbs sampling scheme to sample from the hierarchical model enforcing all constraints.
