Intended for advanced undergraduates and graduate students, this book is a practical guide to the use of probability and statistics in experimental physics. The emphasis is on applications and understanding, on theorems and techniques actually used in research. The text is not a comprehensive text in probability and statistics; proofs are sometimes omitted if they do not contribute to intuition in understanding the theorem. The problems, some with worked solutions, introduce the student to the use of computers; occasional reference is made to routines available in the CERN library, but other systems, such as Maple, can also be used. Topics covered include: basic concepts; definitions; some simple results independent of specific distributions; discrete distributions; the normal and other continuous distributions; generating and characteristic functions; the Monte Carlo method and computer simulations; multi-dimensional distributions; the central limit theorem; inverse probability and confidence belts; estimation methods; curve fitting and likelihood ratios; interpolating functions; fitting data with constraints; robust estimation methods. This second edition introduces a new method for dealing with small samples, such as may arise in search experiments, when the data are of low probability. It also includes a new chapter on queuing problems (including a simple, but useful buffer length example). In addition new sections discuss over- and under-coverage using confidence belts, the extended maximum-likelihood method, the use of confidence belts for discrete distributions, estimation of correlation coefficients, and the effective variance method for fitting y = f(x) when both x and y have measurement errors. A complete Solutions Manual is available.

This book comprises nine selected works on numerical and computational methods for solving multiobjective optimization, game theory, and machine learning problems. It provides extended versions of selected papers from various fields of science such as computer science, mathematics and engineering that were presented at EVOLVE 2013 held in July 2013 at Leiden University in the Netherlands. The internationally peer-reviewed papers include original work on important topics in both theory and applications, such as the role of diversity in optimization, statistical approaches to combinatorial optimization, computational game theory, and cell mapping techniques for numerical landscape exploration. Applications focus on aspects including robustness, handling multiple objectives, and complex search spaces in engineering design and computational biology.

This book covers a range of statistical methods useful in the analysis of medical data, from the simple to the sophisticated, and shows how they may be applied using the latest versions of S-PLUS and S-PLUS 6. In each chapter several sets of medical data are explored and analysed using a mixture of graphical and model fitting approaches. At the end of each chapter the S-PLUS script files are listed, enabling readers to reproduce all the analyses and graphics in the chapter. These script files can be downloaded from a web site. The aim of the book is to show how to use S-PLUS as a powerful environment for undertaking a variety of statistical analyses from simple inference to complex model fitting, and for providing informative graphics. All such methods are of increasing importance in handling data from a variety of medical investigations including epidemiological studies and clinical trials. The mix of real data examples and background theory make this book useful for students and researchers alike. For the former, exercises are provided at the end of each chapter to increase their fluency in using the command line language of the S-PLUS software. Professor Brian Everitt is Head of the Department of Biostatistics and Computing at the Institute of Psychiatry in London and Sophia Rabe-Hesketh is a senior lecturer in the same department. Professor Everitt is the author of over 30 books on statistics including two previously co-authored with Dr. Rabe-Hesketh.

The term singular spectrum comes from the spectral (eigenvalue) decomposition of a matrix A into its set (spectrum) of eigenvalues. These eigenvalues, A, are the numbers that make the matrix A -AI singular. The term singular spectrum analysis* is unfortunate since the traditional eigenvalue decomposition involving multivariate data is also an analysis of the singular spectrum. More properly, singular spectrum analysis (SSA) should be called the analysis of time series using the singular spectrum. Spectral decomposition of matrices is fundamental to much the ory of linear algebra and it has many applications to problems in the natural and related sciences. Its widespread use as a tool for time series analysis is fairly recent, however, emerging to a large extent from applications of dynamical systems theory (sometimes called chaos theory). SSA was introduced into chaos theory by Fraedrich (1986) and Broomhead and King (l986a). Prior to this, SSA was used in biological oceanography by Colebrook (1978). In the digi tal signal processing community, the approach is also known as the Karhunen-Loeve (K-L) expansion (Pike et aI., 1984). Like other techniques based on spectral decomposition, SSA is attractive in that it holds a promise for a reduction in the dimen- * Singular spectrum analysis is sometimes called singular systems analysis or singular spectrum approach. vii viii Preface sionality. This reduction in dimensionality is often accompanied by a simpler explanation of the underlying physics.

The book deals with some of the fundamental issues of risk assessment in grid computing environments. The book describes the development of a hybrid probabilistic and possibilistic model for assessing the success of a computing task in a grid environment

After Karl JAreskog's first presentation in 1970, Structural Equation Modelling or SEM has become a main statistical tool in many fields of science. It is the standard approach of factor analytic and causal modelling in such diverse fields as sociology, education, psychology, economics, management and medical sciences. In addition to an extension of its application area, Structural Equation Modelling also features a continual renewal and extension of its theoretical background. The sixteen contributions to this book, written by experts from many countries, present important new developments and interesting applications in Structural Equation Modelling. The book addresses methodologists and statisticians professionally dealing with Structural Equation Modelling to enhance their knowledge of the type of models covered and the technical problems involved in their formulation. In addition, the book offers applied researchers new ideas about the use of Structural Equation Modeling in solving their problems. Finally, methodologists, mathematicians and applied researchers alike are addressed, who simply want to update their knowledge of recent approaches in data analysis and mathematical modelling.

This book has a collection of articles written by Big Data experts to describe some of the cutting-edge methods and applications from their respective areas of interest, and provides the reader with a detailed overview of the field of Big Data Analytics as it is practiced today. The chapters cover technical aspects of key areas that generate and use Big Data such as management and finance; medicine and healthcare; genome, cytome and microbiome; graphs and networks; Internet of Things; Big Data standards; bench-marking of systems; and others. In addition to different applications, key algorithmic approaches such as graph partitioning, clustering and finite mixture modelling of high-dimensional data are also covered. The varied collection of themes in this volume introduces the reader to the richness of the emerging field of Big Data Analytics.

Linear regression is an important area of statistics, theoretical or applied. There have been a large number of estimation methods proposed and developed for linear regression. Each has its own competitive edge but none is good for all purposes. This manuscript focuses on construction of an adaptive combination of two estimation methods. The purpose of such adaptive methods is to help users make an objective choice and to combine desirable properties of two estimators.

This is the first book on the subject since its introduction more than fifty years ago, and it can be used as a graduate text or as a reference work. It features all of the key results, many very useful tables, and a large number of research problems. The book will be of interest to those interested in one of the most fascinating areas of discrete mathematics, connected to statistics and coding theory, with applications to computer science and cryptography. It will be useful for anyone who is running experiments, whether in a chemistry lab or a manufacturing plant (trying to make those alloys stronger), or in agricultural or medical research. Sam Hedayat is Professor of Statistics and Senior Scholar in the Department of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago. Neil J.A. Sloane is with AT&T Bell Labs (now AT&T Labs). John Stufken is Professor Statistics at Iowa State University.

Principles of Copula Theory explores the state of the art on copulas and provides you with the foundation to use copulas in a variety of applications. Throughout the book, historical remarks and further readings highlight active research in the field, including new results, streamlined presentations, and new proofs of old results. After covering the essentials of copula theory, the book addresses the issue of modeling dependence among components of a random vector using copulas. It then presents copulas from the point of view of measure theory, compares methods for the approximation of copulas, and discusses the Markov product for 2-copulas. The authors also examine selected families of copulas that possess appealing features from both theoretical and applied viewpoints. The book concludes with in-depth discussions on two generalizations of copulas: quasi- and semi-copulas. Although copulas are not the solution to all stochastic problems, they are an indispensable tool for understanding several problems about stochastic dependence. This book gives you the solid and formal mathematical background to apply copulas to a range of mathematical areas, such as probability, real analysis, measure theory, and algebraic structures.

In 1978 Edwin T. Jaynes and Myron Tribus initiated a series of workshops to exchange ideas and recent developments in technical aspects and applications of Bayesian probability theory. The first workshop was held at the University of Wyoming in 1981 organized by C.R. Smith and W.T. Grandy. Due to its success, the workshop was held annually during the last 18 years. Over the years, the emphasis of the workshop shifted gradually from fundamental concepts of Bayesian probability theory to increasingly realistic and challenging applications. The 18th international workshop on Maximum Entropy and Bayesian Methods was held in Garching / Munich (Germany) (27-31. July 1998). Opening lectures by G. Larry Bretthorst and by Myron Tribus were dedicated to one of th the pioneers of Bayesian probability theory who died on the 30 of April 1998: Edwin Thompson Jaynes. Jaynes revealed and advocated the correct meaning of 'probability' as the state of knowledge rather than a physical property. This inter pretation allowed him to unravel longstanding mysteries and paradoxes. Bayesian probability theory, "the logic of science" - as E.T. Jaynes called it - provides the framework to make the best possible scientific inference given all available exper imental and theoretical information. We gratefully acknowledge the efforts of Tribus and Bretthorst in commemorating the outstanding contributions of E.T. Jaynes to the development of probability theory."

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. Limit theorems for semimartingales form the basis of the martingale approximation approach. The methods of martingale approximation addressed in this book pertain to estimates of the rate of convergence in the central limit theorem and in the invariance principle. Some applications of martingale approximation are illustrated by the analysis of U-statistics, rank statistics, statistics of exchangeable variables and stochastic exponential statistics. Simplified results of stochastic analysis are given for use in investigations of many applied problems, including mathematical statistics, financial mathematics, mathematical biology, industrial mathematics and engineering.

The contributions in this book focus on a variety of topics related to discrepancy theory, comprising Fourier techniques to analyze discrepancy, low discrepancy point sets for quasi-Monte Carlo integration, probabilistic discrepancy bounds, dispersion of point sets, pair correlation of sequences, integer points in convex bodies, discrepancy with respect to geometric shapes other than rectangular boxes, and also open problems in discrepany theory.

Digital Image Processing with C++ presents the theory of digital image processing, and implementations of algorithms using a dedicated library. Processing a digital image means transforming its content (denoising, stylizing, etc.), or extracting information to solve a given problem (object recognition, measurement, motion estimation, etc.). This book presents the mathematical theories underlying digital image processing, as well as their practical implementation through examples of algorithms implemented in the C++ language, using the free and easy-to-use CImg library. Chapters cover in a broad way the field of digital image processing and proposes practical and functional implementations of each method theoretically described. The main topics covered include filtering in spatial and frequency domains, mathematical morphology, feature extraction and applications to segmentation, motion estimation, multispectral image processing and 3D visualization. Students or developers wishing to discover or specialize in this discipline, teachers and researchers wishing to quickly prototype new algorithms, or develop courses, will all find in this book material to discover image processing or deepen their knowledge in this field.

VLSI CADhas greatly bene?ted from the use of reduced ordered Binary Decision Diagrams (BDDs) and the clausal representation as a problem of Boolean Satis?ability (SAT), e.g. in logic synthesis, ver- cation or design-for-testability. In recent practical applications, BDDs are optimized with respect to new objective functions for design space exploration. The latest trends show a growing number of proposals to fuse the concepts of BDD and SAT. This book gives a modern presentation of the established as well as of recent concepts. Latest results in BDD optimization are given, c- ering di?erent aspects of paths in BDDs and the use of e?cient lower bounds during optimization. The presented algorithms include Branch ? and Bound and the generic A -algorithm as e?cient techniques to - plore large search spaces. ? The A -algorithm originates from Arti?cial Intelligence (AI), and the EDA community has been unaware of this concept for a long time. Re- ? cently, the A -algorithm has been introduced as a new paradigm to explore design spaces in VLSI CAD. Besides AI search techniques, the book also discusses the relation to another ?eld of activity bordered to VLSI CAD and BDD optimization: the clausal representation as a SAT problem.

Microarrays for simultaneous measurement of redundancy of RNA species are used in fundamental biology as well as in medical research. Statistically, a microarray may be considered as an observation of very high dimensionality equal to the number of expression levels measured on it. In "Statistical Methods for Microarray Data Analysis: Methods and Protocols, " expert researchers in the field detail many methods and techniques used to study microarrays, guiding the reader from microarray technology to statistical problems of specific multivariate data analysis. Written in the highly successful "Methods in Molecular Biology " series format, the chapters include the kind of detailed description and implementation advice that is crucial for getting optimal results in the laboratory.

Thorough and intuitive, "Statistical Methods for Microarray Data Analysis: ""Methods and Protocols "aids scientists in continuing to study microarrays and the most current statistical methods.

This book provides a comprehensive review of environmental benefit transfer methods, issues and challenges, covering topics relevant to researchers and practitioners. Early chapters provide accessible introductory materials suitable for non-economists. These chapters also detail how benefit transfer is used within the policy process. Later chapters cover more advanced topics suited to valuation researchers, graduate students and those with similar knowledge of economic and statistical theory and methods. This book provides the most complete coverage of environmental benefit transfer methods available in a single location. The book targets a wide audience, including undergraduate and graduate students, practitioners in economics and other disciplines looking for a one-stop handbook covering benefit transfer topics and those who wish to apply or evaluate benefit transfer methods. It is designed for those both with and without training in economics

The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models - proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter - which underlie modern survival analysis. Researchers and students alike will find that this text differs from most recent works in that it is mostly concerned with methodological issues rather than the analysis itself.

This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes. Probabilistic properties of associated sequences, demimartingales and related processes are discussed in the first six chapters. Applications of some of these results to some problems in nonparametric statistical inference for such processes are investigated in the last three chapters.

These notes are based on lectures presented during the seminar on " Asymptotic Statistics" held at SchloB Reisensburg, Gunzburg, May 29-June 5, 1988. They consist of two parts, the theory of asymptotic expansions in statistics and probabilistic aspects of the asymptotic distribution theory in nonparametric statistics. Our intention is to provide a comprehensive presentation of these two subjects, leading from elementary facts to the advanced theory and recent results. Prospects for further research are also included. We would like to thank all participants for their stimulating discussions and their interest in the subjects, which made lecturing very pleasant. Special thanks are due H. Zimmer for her excellent typing. We would also like to take this opportunity to to express our thanks to the Gesellschaft fur mathematische Forschung and to the Deutsche Mathematiker Vereinigung, especially to Professor G. Fischer, for the opportunity to present these lectures and to the Birkhauser Verlag for the publication of these lecture notes. R. Bhattacharya, M. Denker Part I: Asymptotic Expansions in Statistics Rabi Bhattacharya 11 1. CRAMER-EDGEWORTH EXPANSIONS Let Q be a probability measure on (IRk, B"), B" denoting the Borel sigmafield on IR". Assume that the s - th absolute moment of Q is finite, (1.1) P. := J II x lis Q(dx) < 00, for some integer s;::: 3, and that Q is normalized, (1.2) J x(i)Q(dx) = 0 (1 ~ i ~ k), J x(i)x(j)Q(dx) = Dij (1 ~ i,j ~ k).

Bayesian Modeling and Computation in Python aims to help beginner Bayesian practitioners to become intermediate modelers. It uses a hands on approach with PyMC3, Tensorflow Probability, ArviZ and other libraries focusing on the practice of applied statistics with references to the underlying mathematical theory. The book starts with a refresher of the Bayesian Inference concepts. The second chapter introduces modern methods for Exploratory Analysis of Bayesian Models. With an understanding of these two fundamentals the subsequent chapters talk through various models including linear regressions, splines, time series, Bayesian additive regression trees. The final chapters include Approximate Bayesian Computation, end to end case studies showing how to apply Bayesian modelling in different settings, and a chapter about the internals of probabilistic programming languages. Finally the last chapter serves as a reference for the rest of the book by getting closer into mathematical aspects or by extending the discussion of certain topics. This book is written by contributors of PyMC3, ArviZ, Bambi, and Tensorflow Probability among other libraries.

This book reports on the latest advances in the analysis of non-stationary signals, with special emphasis on cyclostationary systems. It includes cutting-edge contributions presented at the 7th Workshop on "Cyclostationary Systems and Their Applications," which was held in Grodek nad Dunajcem, Poland, in February 2014. The book covers both the theoretical properties of cyclostationary models and processes, including estimation problems for systems exhibiting cyclostationary properties, and several applications of cyclostationary systems, including case studies on gears and bearings, and methods for implementing cyclostationary processes for damage assessment in condition-based maintenance operations. It addresses the needs of students, researchers and professionals in the broad fields of engineering, mathematics and physics, with a special focus on those studying or working with nonstationary and/or cyclostationary processes.

This book features original research papers presented at the International Conference on Computational and Applied Mathematics, held at the Indian Institute of Technology Kharagpur, India during November 23-25, 2018. This book covers various topics under applied mathematics, ranging from modeling of fluid flow, numerical techniques to physical problems, electrokinetic transport phenomenon, graph theory and optimization, stochastic modelling and machine learning. It introduces the mathematical modeling of complicated scientific problems, discusses micro- and nanoscale transport phenomena, recent development in sophisticated numerical algorithms with applications, and gives an in-depth analysis of complicated real-world problems. With contributions from internationally acclaimed academic researchers and experienced practitioners and covering interdisciplinary applications, this book is a valuable resource for researchers and students in fields of mathematics, statistics, engineering, and health care.

The book is devoted to the new trends in random evolutions and their various applications to stochastic evolutionary sytems (SES). Such new developments as the analogue of Dynkin's formulae, boundary value problems, stochastic stability and optimal control of random evolutions, stochastic evolutionary equations driven by martingale measures are considered. The book also contains such new trends in applied probability as stochastic models of financial and insurance mathematics in an incomplete market. In the famous classical financial mathematics Black-Scholes model of a (B, S) market for securities prices, which is used for the description of the evolution of bonds and stocks prices and also for their derivatives, such as options, futures, forward contracts, etc., it is supposed that the dynamic of bonds and stocks prices are set by a linear differential and linear stochastic differential equations, respectively, with interest rate, appreciation rate and volatility such that they are predictable processes. Also, in the Arrow-Debreu economy, the securities prices which support a Radner dynamic equilibrium are a combination of an Ito process and a random point process, with the all coefficients and jumps being predictable processes."