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.
This book discusses equi-quantile values and their use in generating decision alternatives under the twofold complexities of uncertainty and dependence, offering scope for surrogating between two alternative portfolios when they are correlated. The book begins with a discussion on components of rationality and learning models as indispensable concepts in decision-making processes. It identifies three-fold complexities in such processes: uncertainty, dependence and dynamism. The book is a novel attempt to seek tangible solutions for such decision problems. To do so, four hundred tables of bi-quantile pairs are presented for carefully chosen grids. In fact, it is a two-variable generalization of the inverse normal integral table, which is used in obtaining bivariate normal quantile pairs for the given values of probability and correlation. When making decisions, only two of them have to be taken at a time. These tables are essential tools for decision-making under risk and dependence, and offer scope for delving up to a single step of dynamism. The book subsequently addresses averments dealing with applications and advantages. The content is useful to empirical scientists and risk-oriented decision makers who are often required to make choices on the basis of pairs of variables. The book also helps simulators seeking valid confidence intervals for their estimates, and particle physicists looking for condensed confidence intervals for Higgs–Boson utilizing the Bose–Einstein correlation given the magnitude of such correlations. Entrepreneurs and investors as well as students of management, statistics, economics and econometrics, psychology, psychometrics and psychographics, social sciences, geographic information system, geology, agricultural and veterinary sciences, medical sciences and diagnostics, and remote sensing will also find the book very useful.
This book presents the refereed proceedings of the Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Leuven (Belgium) in April 2014. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics.
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.
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.
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.
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.
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.
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.
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.
