  Modern cancer genomics datasets involve widely varying sizes and scales,
measurement variables, and correlation structures. A fundamental analytical
goal in these high-throughput studies is the development of general statistical
techniques that can cleanly sift the signal from noise in identifying
disease-specific genomic signatures across a set of experimental or biological
conditions. We propose BayesDiff, a nonparametric Bayesian approach based on a
novel class of first order mixture models, called the Sticky Poisson-Dirichlet
process or multicuisine restaurant franchise. The BayesDiff methodology
flexibly utilizes information from all the measurements and adaptively
accommodates any serial dependence in the data, accounting for the inter-probe
distances, to perform simultaneous inferences on the variables. The technique
is applied to analyze a DNA methylation gastrointestinal (GI) cancer dataset,
which displays both serial correlations and complex interaction patterns. Our
analyses and results both support and complement known aspects of DNA
methylation and gene association in upper GI cancers. In simulation studies, we
demonstrate the effectiveness of the BayesDiff procedure relative to existing
techniques for differential DNA methylation.
