Analysis of distributional variation through multi-scale Beta-Binomial   modeling
  Many statistical analyses involve the comparison of multiple data sets collected under different conditions in order to identify the difference in the underlying distributions. A common challenge in multi-sample comparison is the presence of various confounders, or extraneous causes other than the conditions of interest that also contribute to the difference across the distributions. They result in false findings, i.e., identified differences that are not replicable in follow-up investigations. We consider an ANOVA approach to addressing this issue in multi-sample comparison---by collecting replicate data sets under each condition, thereby allowing the identification of the interesting distributional variation from the extraneous ones. We introduce a multi-scale Bayesian hierarchical model for the analysis of distributional variation (ANDOVA) under this design, based on a collection of Beta-Binomial tests targeting variations of different scales at different locations across the sample space. Instead treating the tests independently, the model employs a graphical structure to introduce dependency among the individual tests thereby allowing borrowing of strength among them. We derive efficient inference recipe through a combination of numerical integration and message passing, and evaluate the ability of our method to effectively address ANDOVA through extensive simulation. We utilize our method to analyze a DNase-seq data set for identifying differences in transcriptional factor binding. 
Li Ma and Jacopo Soriano
stat.ME stat.AP stat.CO