Haplotype reconstruction via Bayesian linear models with unknown design

Description

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.

Period	01 Aug 2023
Event title	EcoStat 2023
Event type	Conference
Location	JapanShow on map