Contemporary Mathematics 1991; 276 pp; softcover Volume: 115 ISBN10: 0821851225 ISBN13: 9780821851227 List Price: US$95 Member Price: US$76 Order Code: CONM/115
 High dimensional integration arises naturally in two major subfields of statistics: multivariate and Bayesian statistics. Indeed, the most common measures of central tendency, variation, and loss are defined by integrals over the sample space, the parameter space, or both. Recent advances in computational power have stimulated significant new advances in both Bayesian and classical multivariate statistics. In many statistical problems, however, multiple integration can be the major obstacle to solutions. This volume contains the proceedings of an AMSIMSSIAM Joint Summer Research Conference on Statistical Multiple Integration, held in June 1989 at Humboldt State University in Arcata, California. The conference represents an attempt to bring together mathematicians, statisticians, and computational scientists to focus on the many important problems in statistical multiple integration. The papers document the state of the art in this area with respect to problems in statistics, potential advances blocked by problems with multiple integration, and current work directed at expanding the capability to integrate over high dimensional surfaces. Table of Contents  D. K. Kahaner  A survey of existing multidimensional quadrature routines
 A. Genz  Subregion adaptive algorithms for multiple integrals
 E. de Doncker and J. A. Kapenga  Parallel systems and adaptive integration
 M. Mascagni  Highdimensional numerical integration and massively parallel computing
 R. K. Tsutakawa  Multiple integration in Bayesian psychometrics
 R. E. Kass, L. Tierney, and J. B. Kadane  Laplace's method in Bayesian analysis
 R. L. Wolpert  Monte Carlo integration in Bayesian statistical analysis
 J. Geweke  Generic, algorithmic approaches to Monte Carlo integration in Bayesian inference
 M. Evans  Adaptive importance sampling and chaining
 P. Müller  Monte Carlo integration in general dynamic models
 M.S. Oh  Monte Carlo integration via importance sampling: Dimensionality effect and an adaptive algorithm
 V. Luzar and I. Olkin  Comparison of simulation methods in the estimation of the ordered characteristic roots of a random covariance matrix
 J. F. Monahan and R. F. Liddle  A stationary stochastic approximation method
 Y. L. Tong  Inequalities and bounds for a class of multiple probability integrals, with applications
 V. K. Kaishev  A Gaussian cubature formula for the computation of generalized \(B\)splines and its application to serial correlation
 J. P. Hardwick  Computational problems associated with minimizing the risk in a simple clinical trial
 J. H. Albert  Discussion on papers by Geweke, Wolpert, Evans, Oh, and Kass, Tierney, and Kadane
 R. Shanmugam  Comments on computational conveniences discussed in articles by Evans, Geweke, Müller, and KassTierneyKadane
 I. Olkin  A discussion of papers by Genz, Tsutakawa, and Tong
 N. Flournoy  A discussion of papers by Luzar and Olkin, Kaishev, and Monahan and Liddle
