Prior Specification Sample Clauses

Prior Specification. We employ a Bayesian adaptive structured shrinkage prior formulation similar to Xxxxx et al. (2016) and the goal is to achieve sparse estimations for W and Z while incorporating existing biological information simultaneously. There are multiple com- ponents in this prior. First, a Bayesian Laplacian shrinkage prior is imposed on W: log π(W|λ) = C + X xxx xxx − X xxx|xxx| x,x x,x where λjl is a parameter controlling the shrinkage level of wjl. Unlike standard Lapla- cian prior that uses the same shrinkage parameter λ for all wjl’s, our approach adapts the shrinkage parameter to individual wjl, hence the term of adaptive shrinkage. We further impose a Bayesian shrinkage prior on λ to incorporate biological information, also known as structural information, hence the term of structured shrinkage prior. Suppose the biological information is given through graphs. H graphs Gh = (Ph, Eh) are given where Ph is the set of variables 1, . . . , ph in the h-th dataset and l