  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.
