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Author: STANFORD UNIV CA DEPT OF STATISTICS.
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
The computation of orthant probabilities represents a difficult numerical problem for even modest dimensions. Moran (1984) proposed a Monte Carlo estimator of these quantities. In this paper a more general class of estimators is developed and methods for obtaining efficiency gains over Moran's procedure are discussed. Further, the authors discuss the Monte Carlo evaluation of the multivariate normal distribution function.
Author: STANFORD UNIV CA DEPT OF STATISTICS.
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
The computation of orthant probabilities represents a difficult numerical problem for even modest dimensions. Moran (1984) proposed a Monte Carlo estimator of these quantities. In this paper a more general class of estimators is developed and methods for obtaining efficiency gains over Moran's procedure are discussed. Further, the authors discuss the Monte Carlo evaluation of the multivariate normal distribution function.
Author: Alan Genz
Publisher: Springer Science & Business Media
ISBN: 3642016898
Category : Computers
Languages : en
Pages : 130
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Book Description
Multivariate normal and t probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications.
Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 0387216103
Category : Computers
Languages : en
Pages : 387
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Book Description
Monte Carlo simulation has become one of the most important tools in all fields of science. Simulation methodology relies on a good source of numbers that appear to be random. These "pseudorandom" numbers must pass statistical tests just as random samples would. Methods for producing pseudorandom numbers and transforming those numbers to simulate samples from various distributions are among the most important topics in statistical computing. This book surveys techniques of random number generation and the use of random numbers in Monte Carlo simulation. The book covers basic principles, as well as newer methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo. The best methods for generating random variates from the standard distributions are presented, but also general techniques useful in more complicated models and in novel settings are described. The emphasis throughout the book is on practical methods that work well in current computing environments. The book includes exercises and can be used as a test or supplementary text for various courses in modern statistics. It could serve as the primary test for a specialized course in statistical computing, or as a supplementary text for a course in computational statistics and other areas of modern statistics that rely on simulation. The book, which covers recent developments in the field, could also serve as a useful reference for practitioners. Although some familiarity with probability and statistics is assumed, the book is accessible to a broad audience. The second edition is approximately 50% longer than the first edition. It includes advances in methods for parallel random number generation, universal methods for generation of nonuniform variates, perfect sampling, and software for random number generation.
Author: Giang B. Trinh
Publisher:
ISBN: 9781303242007
Category :
Languages : en
Pages :
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Book Description
We introduce algorithms for block LDLt decompositions of positive definite covariance matrices. These are extensions of the LDLt decomposition which requires D to be a diagonal matrix. We make use of these algorithms to represent the mutivariate normal (MVN) probability as a bivariate-iterated, trivariate-iterated and multivariate-iterated integrals. From there, we introduce a new method of approximating and simulating MVN probabilities using bivariate conditioning with simulation. Basic algorithms for bivariate, trivariate, multivariate conditioning are derived. A new approximate formula for multivariate normal probabilities which uses a product of bivariate normal probabilities is derived and considered with different variance reduction techniques. The new method is compared with approximation methods based on products of univariate normal probabilities. The new method uses conditioning with a sequence of truncated bivariate probabilities. Simulation methods which use Monte Carlo, and quasi-Monte Carlo point sets are developed.
Author: Elizabeth N. Abbe
Publisher:
ISBN:
Category : Monte Carlo method
Languages : en
Pages : 44
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Book Description
Author: J. Hammersley
Publisher: Springer Science & Business Media
ISBN: 9400958196
Category : Science
Languages : en
Pages : 184
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Book Description
This monograph surveys the present state of Monte Carlo methods. we have dallied with certain topics that have interested us Although personally, we hope that our coverage of the subject is reasonably complete; at least we believe that this book and the references in it come near to exhausting the present range of the subject. On the other hand, there are many loose ends; for example we mention various ideas for variance reduction that have never been seriously appli(:d in practice. This is inevitable, and typical of a subject that has remained in its infancy for twenty years or more. We are convinced Qf:ver theless that Monte Carlo methods will one day reach an impressive maturity. The main theoretical content of this book is in Chapter 5; some readers may like to begin with this chapter, referring back to Chapters 2 and 3 when necessary. Chapters 7 to 12 deal with applications of the Monte Carlo method in various fields, and can be read in any order. For the sake of completeness, we cast a very brief glance in Chapter 4 at the direct simulation used in industrial and operational research, where the very simplest Monte Carlo techniques are usually sufficient. We assume that the reader has what might roughly be described as a 'graduate' knowledge of mathematics. The actual mathematical techniques are, with few exceptions, quite elementary, but we have freely used vectors, matrices, and similar mathematical language for the sake of conciseness.
Author: Ming-Hui Chen
Publisher: Springer Science & Business Media
ISBN: 1461212766
Category : Mathematics
Languages : en
Pages : 399
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Book Description
Dealing with methods for sampling from posterior distributions and how to compute posterior quantities of interest using Markov chain Monte Carlo (MCMC) samples, this book addresses such topics as improving simulation accuracy, marginal posterior density estimation, estimation of normalizing constants, constrained parameter problems, highest posterior density interval calculations, computation of posterior modes, and posterior computations for proportional hazards models and Dirichlet process models. The authors also discuss model comparisons, including both nested and non-nested models, marginal likelihood methods, ratios of normalizing constants, Bayes factors, the Savage-Dickey density ratio, Stochastic Search Variable Selection, Bayesian Model Averaging, the reverse jump algorithm, and model adequacy using predictive and latent residual approaches. The book presents an equal mixture of theory and applications involving real data, and is intended as a graduate textbook or a reference book for a one-semester course at the advanced masters or Ph.D. level. It will also serve as a useful reference for applied or theoretical researchers as well as practitioners.
Author: Samuel Kotz
Publisher: John Wiley & Sons
ISBN: 0471654035
Category : Mathematics
Languages : en
Pages : 752
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Book Description
Continuous Multivariate Distributions, Volume 1, Second Edition provides a remarkably comprehensive, self-contained resource for this critical statistical area. It covers all significant advances that have occurred in the field over the past quarter century in the theory, methodology, inferential procedures, computational and simulational aspects, and applications of continuous multivariate distributions. In-depth coverage includes MV systems of distributions, MV normal, MV exponential, MV extreme value, MV beta, MV gamma, MV logistic, MV Liouville, and MV Pareto distributions, as well as MV natural exponential families, which have grown immensely since the 1970s. Each distribution is presented in its own chapter along with descriptions of real-world applications gleaned from the current literature on continuous multivariate distributions and their applications.
Author: Michael Evans
Publisher: OUP Oxford
ISBN: 019158987X
Category : Mathematics
Languages : en
Pages : 302
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Book Description
This book is designed to introduce graduate students and researchers to the primary methods useful for approximating integrals. The emphasis is on those methods that have been found to be of practical use, and although the focus is on approximating higher- dimensional integrals the lower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques as well as a complete development of Monte Carlo algorithms. For the Monte Carlo section importance sampling methods, variance reduction techniques and the primary Markov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and hence provides an accessible textbook and reference for researchers in a wide variety of disciplines.
Author: T. Takahashi
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
