Integrals play an important role in a wide variety of practical statistical calculations. They give means, covariances, and various kinds of conditional and unconditional probabilities. Many of these integrals are defined over regions in multiple dimensions, and they do not have values that can be obtained from formulas or tables. Integrals of this type must be estimated numerically, often using computationally intensive algorithms. More efficient methods will be developed in this research for the numerical computation of multiple integrals that arise in statistical computations. Attention will be focused on the use of subregion adaptive algorithms and better algorithms of this type will be developed through the use of specialized transformation techniques and better basic integrations rules that take account of the particular features of statistical integration problems. The algorithms will be implemented in public domain software which will be made available over electronic mail networks and interfaced to the S system for statistical computation on scientific workstations.
