Material for “ DGEclust : differential expres - sion analysis of clustered count data ”

Introduction In this Supplementary Material, we provide the mathematical details of the algorithm we used to make posterior inferences on the generative model described by Eqs. 5. Currently, there are two major classes of methods for posterior inference in Hierarchical Dirichlet Process Mixture Models. The first class includes algorithms based on the Chinese Restaurant metaphor for representing the Dirichlet Process, as for example in [1, 2]. The second class includes variational inference approaches in either a batch or an online data processing context, as for example in [3]. The algorithm we present here is an extension of the blocked Gibbs sampler in [4] (which was developed for non-–hierarchical Dirichlet Process mixture models) in the case of non–conjugate Hierarchical Dirichlet Process mixtures. Unlike variational methodologies, it approximates exact posteriors and, unlike approaches based on the Chinese Restaurant metaphor, it follows a blocked sampling strategy, which permits, in principle, faster convergence, and parallel implementation on multicore processors, which opens the possibility for applications on large gene expression datasets. The first step in developing this algorithm is to cast the implicit generative model summarised in Eqs. 5 in an equivalent, explicit form, which makes use of Sethuraman’s constructive representation of a draw from