**Contemporary Mathematics**

Volume: 115;
1991;
276 pp;
Softcover

MSC: Primary 62; 65;
Secondary 00

Print ISBN: 978-0-8218-5122-7

Product Code: CONM/115

List Price: $95.00

Individual Member Price: $76.00

**Electronic ISBN: 978-0-8218-7703-6
Product Code: CONM/115.E**

List Price: $95.00

Individual Member Price: $76.00

# Statistical Multiple Integration

Share this page *Edited by *
*Nancy Flournoy; Robert Tsutakawa*

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

## Statistical Multiple Integration

- Contents ix10 free
- Introduction 114 free
- A Survey of Existing Multidimensional Quadrature Routines 922
- Subregion Adaptive Algorithms for Multiple Integrals 2336
- Parallel Systems and Adaptive Integration 3346
- High-Dimensional Numerical Integration and Massively Parallel Computing 5366
- Multiple Integration in Bayesian Psychometrics 7588
- Laplace's Method in Bayesian Analysis 89102
- Monte Carlo Integration in Bayesian Statistical Analysis 101114
- Generic, Algorithmic Approaches to Monte Carlo Integration in Bayesian Inference 117130
- Adaptive Importance Sampling and Chaining 137150
- Monte Carlo Integration in General Dynamic Models 145158
- Monte Carlo Integration via Importance Sampling: Dimensionality Effect and an Adaptive Algorithm 165178
- Comparison of Simulation Methods in the Estimation of the Ordered Characteristic Roots of a Random Covariance Matrix 189202
- A Stationary Stochastic Approximation Method 203216
- Inequalities and Bounds for a Class of Multiple Probability Integrals, with Applications 209222
- A Gaussian Cubature Formula for the Computation of Generalized B-splines and its Application to Serial Correlation 219232
- Computational Problems Associated with Minimizing the Risk in a Simple Clinical Trial 239252
- Discussion on Papers by Geweke, Wolpert, Evans, Oh, and Kass, Tierney, and Kadane 257270
- Comments on Computational Conveniences Discussed in the Articlesby Evans, Geweke, Mi.iller, and Kass-Tierney-Kadane 261274
- A Discussion of Papers by Genz, Tsutakawa, and Tong 271284
- A Discussion of Papers by Luzar and Olkin, Kaishev, and Monahan and Liddle 273286