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Statistical Multiple Integration
Edited by: Nancy Flournoy and Robert K. Tsutakawa
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Contemporary Mathematics
1991; 276 pp; softcover
Volume: 115
ISBN-10: 0-8218-5122-5
ISBN-13: 978-0-8218-5122-7
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 AMS-IMS-SIAM 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.

• 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 -- High-dimensional 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 Kass-Tierney-Kadane
• 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