Adaptive Task Partitioning for Bayesian Applications

The numerical integration of the posterior in Bayesian analysis leads to a class of multivariate integration problems where the integrand has a dominant peak. As Monte-Carlo integration is inadequate, various techniques have been proposed in the literature, involving substantial reformulation with additional analysis, or transformations requiring additional problem parameters. We resort to a black-box approach provided by the ParInt multivariate integration package, which is layered over MPI to run on a distributed system, and utilizes adaptive task partitioning with load balancing to keep high-error subregions distributed over the processes. The performance of the algorithm is demonstrated by detailed test results for Bayesian integrals arising as posterior expectations in linear modeling and for cross-classifications in medical data.