Electronic ISBN:  9780821877036 
Product Code:  CONM/115.E 
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Book DetailsContemporary MathematicsVolume: 115; 1991; 276 ppMSC: Primary 62; 65; Secondary 00;
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

Articles

James Berger  Introduction

D. K. Kahaner  A survey of existing multidimensional quadrature routines [ MR 1117045 ]

Alan Genz  Subregion adaptive algorithms for multiple integrals [ MR 1117046 ]

E. de Doncker and J. A. Kapenga  Parallel systems and adaptive integration [ MR 1117047 ]

Michael Mascagni  Highdimensional numerical integration and massively parallel computing [ MR 1117048 ]

Robert K. Tsutakawa  Multiple integration in Bayesian psychometrics [ MR 1117049 ]

Robert E. Kass, Luke Tierney and Joseph B. Kadane  Laplace’s method in Bayesian analysis

Michael Evans  Adaptive importance sampling and chaining [ MR 1117053 ]

Peter Müller  Monte Carlo integration in general dynamic models [ MR 1117054 ]

ManSuk Oh  Monte Carlo integration via importance sampling: dimensionality effect and an adaptive algorithm [ MR 1117055 ]

Vesna Lužar and Ingram Olkin  Comparison of simulation methods in the estimation of the ordered characteristic roots of a random covariance matrix [ MR 1117056 ]

John F. Monahan and Roger F. Liddle  A stationary stochastic approximation method [ MR 1117057 ]

Y. L. Tong  Inequalities and bounds for a class of multiple probability integrals, with applications [ MR 1117058 ]

V. K. Kaishev  A Gaussian cubature formula for the computation of generalized $B$splines and its application to serial correlation [ MR 1117059 ]

J. P. Hardwick  Computational problems associated with minimizing the risk in a simple clinical trial [ MR 1117060 ]

James H. Albert  Discussion on Papers by Geweke, Wolpert, Evans, Oh, and Kass, Tierney, and Kadane

Ramalingam Shanmugam  Comments on Computational Conveniences Discussed in the Articles by Evans, Geweke, Müller, and KassTierneyKadane

Ingram Olkin  A Discussion of Papers by Genz, Tsutakawa, and Tong

Nancy Flournoy  A Discussion of Papers by Luzar and Olkin, Kaishev, and Monahan and Liddle


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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.

Articles

James Berger  Introduction

D. K. Kahaner  A survey of existing multidimensional quadrature routines [ MR 1117045 ]

Alan Genz  Subregion adaptive algorithms for multiple integrals [ MR 1117046 ]

E. de Doncker and J. A. Kapenga  Parallel systems and adaptive integration [ MR 1117047 ]

Michael Mascagni  Highdimensional numerical integration and massively parallel computing [ MR 1117048 ]

Robert K. Tsutakawa  Multiple integration in Bayesian psychometrics [ MR 1117049 ]

Robert E. Kass, Luke Tierney and Joseph B. Kadane  Laplace’s method in Bayesian analysis

Michael Evans  Adaptive importance sampling and chaining [ MR 1117053 ]

Peter Müller  Monte Carlo integration in general dynamic models [ MR 1117054 ]

ManSuk Oh  Monte Carlo integration via importance sampling: dimensionality effect and an adaptive algorithm [ MR 1117055 ]

Vesna Lužar and Ingram Olkin  Comparison of simulation methods in the estimation of the ordered characteristic roots of a random covariance matrix [ MR 1117056 ]

John F. Monahan and Roger F. Liddle  A stationary stochastic approximation method [ MR 1117057 ]

Y. L. Tong  Inequalities and bounds for a class of multiple probability integrals, with applications [ MR 1117058 ]

V. K. Kaishev  A Gaussian cubature formula for the computation of generalized $B$splines and its application to serial correlation [ MR 1117059 ]

J. P. Hardwick  Computational problems associated with minimizing the risk in a simple clinical trial [ MR 1117060 ]

James H. Albert  Discussion on Papers by Geweke, Wolpert, Evans, Oh, and Kass, Tierney, and Kadane

Ramalingam Shanmugam  Comments on Computational Conveniences Discussed in the Articles by Evans, Geweke, Müller, and KassTierneyKadane

Ingram Olkin  A Discussion of Papers by Genz, Tsutakawa, and Tong

Nancy Flournoy  A Discussion of Papers by Luzar and Olkin, Kaishev, and Monahan and Liddle