Appendixof"T-LoHo: ABayesianRegularization ModelforStructuredSparsityandSmoothnesson Graphs "

For step 1-c (change),Π? is proposed by successively performing split and merge steps. For step 1-a (split), letλold be a local shrinkage parameter of the splitting clusterCold. Note that X = XΦ> is a function ofΠ since Π determines Φ. Line (A3) can be decomposed into a likelihood part|Σ| 1/2(y>Σ 1y/2) n/2 and a prior part For step 1-d (hyper), conditioning on the current partition,Πdivides the edge setE ofGinto the between-cluster edge setEb and within-cluster edge setEw. It is evident to see the computational benefits of using Cholesky factorR. In (A5),|R|is simply a product of its diagonal elements.