A Bayesian test for Hardy–Weinberg equilibrium of biallelic X-chromosomal markers

The X chromosome is a relatively large chromosome, harboring a lot of genetic information. Much of the statistical analysis of X-chromosomal information is complicated by the fact that males only have one copy. Recently, frequentist statistical tests for Hardy–Weinberg equilibrium have been proposed specifically for dealing with markers on the X chromosome. Bayesian test procedures for Hardy–Weinberg equilibrium for the autosomes have been described, but Bayesian work on the X chromosome in this context is lacking. This paper gives the first Bayesian approach for testing Hardy–Weinberg equilibrium with biallelic markers at the X chromosome. Marginal and joint posterior distributions for the inbreeding coefficient in females and the male to female allele frequency ratio are computed, and used for statistical inference. The paper gives a detailed account of the proposed Bayesian test, and illustrates it with data from the 1000 Genomes project. In that implementation, a novel approach to tackle multiple testing from a Bayesian perspective through posterior predictive checks is used.