Simulation of hyper-inverse Wishart distributions in graphical models

We introduce and exemplify an efficient method for direct samplingfrom hyper-inverse Wishart distributions. The method reliesvery naturally on the use of standard junction-tree representationof graphs, and couples these with matrix results for inverseWishart distributions. We describe the theory and resultingcomputational algorithms for both decomposable and nondecomposablegraphical models. An example drawn from financial time seriesdemonstrates application in a context where inferences on astructured covariance model are required. We discuss and investigatequestions of scalability of the simulation methods to higher-dimensionaldistributions. The paper concludes with general comments aboutthe approach, including its use in connection with existingMarkov chain Monte Carlo methods that deal with uncertaintyabout the graphical model structure.