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Statistical Multiple Integration
 
Statistical Multiple Integration
eBook ISBN:  978-0-8218-7703-6
Product Code:  CONM/115.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Statistical Multiple Integration
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Statistical Multiple Integration
eBook ISBN:  978-0-8218-7703-6
Product Code:  CONM/115.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1151991; 276 pp
    MSC: 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 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.

  • 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 — High-dimensional 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 ]
    • Man-Suk 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 Kass-Tierney-Kadane
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1151991; 276 pp
MSC: 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 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.

  • 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 — High-dimensional 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 ]
  • Man-Suk 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 Kass-Tierney-Kadane
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
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