Download or read book Computation of Multivariate Normal and t Probabilities written by Alan Genz and published by Springer Science & Business Media. This book was released on 2009-07-09 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computation Of Multivariate Normal And T Probabilities written by P. Diggle P. Bickel (S. Fienberg, U. Gather) and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo Computation of Some Multivariate Normal Probabilities written by STANFORD UNIV CA DEPT OF STATISTICS. and published by . This book was released on 1987 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computation of Multivariate Normal Probabilities Using Bivariate Conditioning with Simulation written by Giang B. Trinh and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Probability Integrals of Multivariate Normal and Multivariate T written by S. S. Gupta and published by . This book was released on 1962 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper gives a survey of the work on multivariate probability integral and related functions starting with the bivariate case and includes the author's recent work on the probability integrals of the multivariate normal and a multivariate analogue of Student's t. An annotated bibliography on evaluation of multivariate normal and t probability integrals (189 entries) is included. (Author).
Download or read book Multivariate T Distributions and Their Applications written by Samuel Kotz and published by Cambridge University Press. This book was released on 2004-02-16 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost all the results available in the literature on multivariate t-distributions published in the last 50 years are now collected together in this comprehensive reference. Because these distributions are becoming more prominent in many applications, this book is a must for any serious researcher or consultant working in multivariate analysis and statistical distributions. Much of this material has never before appeared in book form. The first part of the book emphasizes theoretical results of a probabilistic nature. In the second part of the book, these are supplemented by a variety of statistical aspects. Various generalizations and applications are dealt with in the final chapters. The material on estimation and regression models is of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.
Download or read book Sparse Grids and Applications Munich 2012 written by Jochen Garcke and published by Springer Science & Business Media. This book was released on 2014-04-11 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse grids make it possible to overcome the “curse” of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparse grids and applications, demonstrating once again the importance of this numerical discretization scheme. The selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures, and the range of applications extends to uncertainty quantification settings and clustering, to name but a few examples.
Download or read book Advances in Reliability and Optimization of Structural Systems written by Dan M. Frangopol and published by CRC Press. This book was released on 2005-12-22 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains thirty-one papers presented at the Twelfth Scientific Meeting of the IFIP Working Group on Reliability and Optimization of Structural Systems which took place in Aalborg, Denmark, from May 22-25, 2005. The Working Group Conference was organized by the IFIP (International Federation for Information Processing) Working Group 7.5 of the Technical Committee on Modelling and Optimization. The purpose of the Working Group is to promote modern structural system reliability and optimization theory and its applications, to stimulate research, development and application of structural system reliability and optimization theory, to assist and advance research and development in these fields, to further the dissemination and exchange of information on reliability and optimization of structural systems, and to encourage education in structural system reliability and optimization theory.
Download or read book Multivariate Normal Distribution The Theory And Applications written by Thu Pham-gia and published by World Scientific. This book was released on 2021-05-05 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with user-friendly applications of normal distribution. In several variables it is called the multinormal distribution which is often handled using matrices for convenience. The author seeks to make the arguments less abstract and hence, starts with the univariate case and moves progressively toward the vector and matrix cases. The approach used in the book is a gradual one, going from one scalar variable to a vector variable and to a matrix variable. The author presents the unified aspect of normal distribution, as well as addresses several other issues, including random matrix theory in physics. Other well-known applications, such as Herrnstein and Murray's argument that human intelligence is substantially influenced by both inherited and environmental factors, will be discussed in this book. It is a better predictor of many personal dynamics — including financial income, job performance, birth out of wedlock, and involvement in crime — than are an individual's parental socioeconomic status, or education level, and deserve to be mentioned and discussed.
Download or read book Continuous Bivariate Distributions written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2009-05-31 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with a review of general developments relating to bivariate distributions, this volume also covers copulas, a subject which has grown immensely in recent years. In addition, it examines conditionally specified distributions and skewed distributions.
Download or read book Normal and Student s t Distributions and Their Applications written by Mohammad Ahsanullah and published by Springer Science & Business Media. This book was released on 2014-02-07 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.
Download or read book High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Download or read book Simultaneous Inference in Regression written by Wei Liu and published by CRC Press. This book was released on 2010-10-19 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simultaneous confidence bands enable more intuitive and detailed inference of regression analysis than the standard inferential methods of parameter estimation and hypothesis testing. Simultaneous Inference in Regression provides a thorough overview of the construction methods and applications of simultaneous confidence bands for various inferentia
Download or read book Learning and Intelligent Optimization written by Giuseppe Nicosia and published by Springer. This book was released on 2013-11-26 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 7th International Conference on Learning and Optimization, LION 7, which was held in Catania, Italy, in January 2013. The 49 contributions presented in this volume were carefully reviewed and selected from 101 submissions. They explore the intersections and uncharted territories between machine learning, artificial intelligence, mathematical programming and algorithms for hard optimization problems.
Download or read book Simultaneous Statistical Inference written by Thorsten Dickhaus and published by Springer Science & Business Media. This book was released on 2014-01-23 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph will provide an in-depth mathematical treatment of modern multiple test procedures controlling the false discovery rate (FDR) and related error measures, particularly addressing applications to fields such as genetics, proteomics, neuroscience and general biology. The book will also include a detailed description how to implement these methods in practice. Moreover new developments focusing on non-standard assumptions are also included, especially multiple tests for discrete data. The book primarily addresses researchers and practitioners but will also be beneficial for graduate students.
Download or read book Applications of Evolutionary Computation written by Giovanni Squillero and published by Springer. This book was released on 2017-04-03 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two volumes LNCS 10199 and 10200 constitute the refereed conference proceedings of the 20th European Conference on the Applications of Evolutionary Computation, EvoApplications 2017, held in Amsterdam, The Netherlands, in April 2017, collocated with the Evo* 2016 events EuroGP, EvoCOP, and EvoMUSART. The 46 revised full papers presented together with 26 poster papers were carefully reviewed and selected from 108 submissions. EvoApplications 2016 consisted of the following 13 tracks: EvoBAFIN (natural computing methods in business analytics and finance), EvoBIO (evolutionary computation, machine learning and data mining in computational biology), EvoCOMNET (nature-inspired techniques for telecommunication networks and other parallel and distributed systems), EvoCOMPLEX (evolutionary algorithms and complex systems), EvoENERGY (evolutionary computation in energy applications), EvoGAMES (bio-inspired algorithms in games), EvoIASP (evolutionary computation in image analysis, signal processing, and pattern recognition), EvoINDUSTRY (nature-inspired techniques in industrial settings), EvoKNOW (knowledge incorporation in evolutionary computation), EvoNUM (bio-inspired algorithms for continuous parameter optimization), EvoPAR (parallel implementation of evolutionary algorithms), EvoROBOT (evolutionary robotics), EvoSET (nature-inspired algorithms in software engineering and testing), and EvoSTOC (evolutionary algorithms in stochastic and dynamic environments).
Download or read book Gaussian Processes for Machine Learning written by Carl Edward Rasmussen and published by MIT Press. This book was released on 2005-11-23 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
