Bayesian Manifold-Constrained-Prior Model for an Experiment to Locate Xce

We propose an analysis for a novel experiment intended to locate the genetic locus Xce (X-chromosome controlling element), which biases the stochastic process of X-inactivation in the mouse. X-inactivation bias is a phenomenon where cells in the embryo randomly choose one parental chromosome to inactivate, but show an average bias towards one parental strain. Measurement of allele-specific gene-expression through pyrosequencing was conducted on mouse crosses of an uncharacterized parent with known carriers. Our Bayesian analysis is suitable for this adaptive experimental design, accounting for the biases and differences in precision among genes. Model identifiability is facilitated by priors constrained to a manifold. We show that reparameterized slice-sampling can suitably tackle a general class of constrained priors. We demonstrate a physical model, based upon a weighted-coin hypothesis, that predicts X-inactivation ratios in untested crosses. This model suggests that Xce alleles differ due to a process known as copy number variation, where stronger Xce alleles are shorter sequences.