This research focuses on the efficient evaluation of multidimensional integrals that arise in Bayesian analysis. The basic approach is first to select a problem-specific transformation to precondition the integrands, and then to use an adaptive integration method. The primary objective now is to investigate how best to choose transformations which will allow adaptive numerical integration algorithms to be used effectively. So far, transformations based on a modal approximation transformation have been shown to reduce computation time significantly for some problems. These approximations need to be refined and tested on practical statistical problems and made to interface with standard statistical software packages. Integrals play a very important role in a wide variety of practical statistical calculations; but often these integrals are defined over regions in multiple dimension and do not have values that can be obtained from formulas or tables. In this case, the integrals must be estimated numerically, often with time intensive computation. New methods and refinements to be developed here will take account of special features of these statistical problems to give efficient adaptive integration algorithms.
