Probability and statistics Books

Book SynopsisStein's startling technique for deriving probability approximations first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This volume, the proceedings of a workshop held in honour of Charles Stein in Singapore, August 2003, contains contributions from many of the mathematicians at the forefront of this effort. It provides a cross-section of the work currently being undertaken, with many pointers to future directions. The papers in the collection include applications to the study of random binary search trees, Brownian motion on manifolds, Monte-Carlo integration, Edgeworth expansions, regenerative phenomena, the geometry of random point sets, and random matrices.Table of ContentsZero Biasing in One and Higher Dimensions, and Applications (L Goldstein & G Reinert); Poisson Limit Theorems for the Appearances of Attributes (O Chryssaphinou et al.); Normal Approximation in Geometric Probability (M D Penrose & J E Yukich); Stein's Method, Edgeworth's Expansions and a Formula of Barbour (V Rotar); Stein's Method for Compound Poisson Approximation (A Xia); The Independence Number for Minimal Spanning Trees (S Lee & Z Su); Strong Memoryless Times (T Erhardsson); Multivariate Poisson-Binomial Approximation (A D Barbour); A BerryEsseen Bound for the t-Statistic (Q-M Shao); An Application of Stein's Method to Maxima in Hypercubes (Z D Bai et al.); Expected Length of an MST (J A Fill & J M Steele); Spectra of Random Matrices with Martingale Structure (F G�tze & A Tikhomirov); Characterization of Brownian Motion on Manifolds (E P Hsu); On Some Randomized Quadrature Rules (W-L Loh); Matrix Correlation Statistics (A D Barbour & L Chen); Random Binary Search Trees (L Devroye).

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Book SynopsisA common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.Trade Review"All the lectures have been given by eminent experts working in the area of Stein's method and provide details and unsolved problems along with a list of very useful references. These lectures will be very valuable for both experts and researchers wishing to explore the powerful approximation method proposed by Charles Stein."Mathematical ReviewsTable of ContentsStein's Method for Normal Approximation (L Chen & Q-M Shao); Stein's Method for Poisson and Compound Poisson Approximation (T Erhardsson); Stein's Method and Poisson Process Approximation (A Xia); Three General Approaches to Stein's Method (G Reinert).

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Book SynopsisThis is the very first comprehensive monograph in a burgeoning, new research area — the theory of cooperative game with incomplete information with emphasis on the solution concept of Bayesian incentive compatible strong equilibrium that encompasses the concept of the Bayesian incentive compatible core. Built upon the concepts and techniques in the classical static cooperative game theory and in the non-cooperative Bayesian game theory, the theory constructs and analyzes in part the powerful n-person game-theoretical model characterized by coordinated strategy-choice with individualistic incentives, the influence of outsiders' strategy choice upon the feasibility and implications of coalitional attainability, and incomplete information. The book presents the basic results of this theory. It also presents the research results to date on the simple, but central economic model of Bayesian pure exchange economy, and also on an alternative approach, anonymous coalition formation.The theory presented here points to an important future research direction in economics. In particular, it has the potential to provide game-theoretical foundations of organizational analysis in which organizations (coalitions) as corporations institute a non-market resource allocation mechanism while using the market resource allocation mechanism at the same time.The book provides appraisals of the various concepts, setups and results established to date as well as many discussions on philosophical issues on different approaches in the area, thereby clarifying the applicability and limitations of the current theory. It also contains numerous examples illustrating various concepts and points of discussions.Cooperative Extensions of the Bayesian Game is an essential reference in strategic cooperative game theory, and serves as an informative textbook for PhD courses in advanced economic theory, mathematical economics, game theory, and industrial organization.

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Book SynopsisThe simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results — mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.Since the first edition was published in 1990, a number of new results have appeared in the literature. The original edition contained many unsolved problems and conjectures which have since been settled; this second revised and enlarged edition includes those new results. Three new chapters have been added: frequently and rarely visited points, heavy points and long excursions. This new edition presents the most complete study of, and the most elementary way to study, the path properties of the Brownian motion.Trade Review"This book tells a very personal and exciting story from the point of view of one of the dominant contributors to the study of random walks, and will be of interest to those looking for intriguing open problems in the theory of random walks and associated strong limit laws." Mathematical Reviews "The reader interested in the theory of random walks in non-random environments and also on the associated strong limit laws will find this book very interesting and also very useful." Zentralblatt MATH

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Book SynopsisThis book is meant for postgraduate modules that cover lifetime data in reliability and survival analysis as taught in statistics, engineering statistics and medical statistics courses. It is helpful for researchers who wish to choose appropriate models and methods for analyzing lifetime data. There is an extensive discussion on the concept and role of ageing in choosing appropriate models for lifetime data, with a special emphasis on tests of exponentiality. There are interesting contributions related to the topics of ageing, tests for exponentiality, competing risks and repairable systems. A special feature of this book is that it introduces the public domain R-software and explains how it can be used in computations of methods discussed in the book.Trade Review"One of the main strengths of this book is that it introduces the public domain R software and nicely explains how it can be used in computations of methods presented in the book ... the monograph would be useful to some applied researchers in related fields." Technometrics

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Book SynopsisThis book is meant for postgraduate modules that cover lifetime data in reliability and survival analysis as taught in statistics, engineering statistics and medical statistics courses. It is helpful for researchers who wish to choose appropriate models and methods for analyzing lifetime data. There is an extensive discussion on the concept and role of ageing in choosing appropriate models for lifetime data, with a special emphasis on tests of exponentiality. There are interesting contributions related to the topics of ageing, tests for exponentiality, competing risks and repairable systems. A special feature of this book is that it introduces the public domain R-software and explains how it can be used in computations of methods discussed in the book.Trade Review"One of the main strengths of this book is that it introduces the public domain R software and nicely explains how it can be used in computations of methods presented in the book ... the monograph would be useful to some applied researchers in related fields." Technometrics

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Book SynopsisThe first edition of this classic book has become the authoritative reference for physicists desiring to master the finer points of statistical data analysis. This second edition contains all the important material of the first, much of it unavailable from any other sources. In addition, many chapters have been updated with considerable new material, especially in areas concerning the theory and practice of confidence intervals, including the important Feldman-Cousins method. Both frequentist and Bayesian methodologies are presented, with a strong emphasis on techniques useful to physicists and other scientists in the interpretation of experimental data and comparison with scientific theories. This is a valuable textbook for advanced graduate students in the physical sciences as well as a reference for active researchers.Trade Review"I highly recommend that this book be kept on every desk -- for consultation when a question arises, for browsing when in the mood to learn something interesting, and for a straight read-though to get a grounding in the classical theory of statistics from an experimental physicist's perspective."CERN CourierTable of ContentsBasic Concepts in Probability; Convergence and the Law of Large Numbers; Probability Distributions; Information; Decision Theory; Theory of Estimators; Point Estimation in Practice; Interval Estimation; Test of Hypotheses; Goodness-of-Fit Tests.

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Book SynopsisTwo features of Processing Random Data differentiate it from other similar books: the focus on computing the reproducibility error for statistical measurements, and its comprehensive coverage of Maximum Likelihood parameter estimation techniques. The book is useful for dealing with situations where there is a model relating to the input and output of a process, but with a random component, which could be noise in the system or the process itself could be random, like turbulence. Parameter estimation techniques are shown for many different types of statistical models, including joint Gaussian. The Cramer-Rao bounds are described as useful estimates of reproducibility errors.Finally, using an example with a random sampling of turbulent flows that can occur when using laser anemometry the book also explains the use of conditional probabilities.Table of ContentsBasic Statistical Concepts; Measurement of Random Variables; Time Series; Parameter Estimation; Random Sampling.

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Book SynopsisThis volume is a collection of papers in celebration of the 80th birthday of Yuan-Shih Chow, whose influential work in probability and mathematical statistics has contributed greatly to mathematics education and the development of statistics research and application in Taiwan and mainland China.The twenty-two papers cover a wide range of problems reflecting both the broad scope of areas where Professor Chow has made major contributions and recent advances in probability theory and statistics.Table of ContentsMaximizing Expected Value with Two Stage Stopping Rules (D Assaf et al.); A Study of Inverses of Thinned Renewal Processes (W-J Huang & C-D Huang); On Dirichlet Multinomial Distributions (R W Keener & W B Wu); The Optimal Stopping Problem for Sn/n and Its Ramifications (T L Lai & Y-C Yao); Bold Play and the Optimal Policy for Vardi's Casino (L Shepp); The Upper Limit of a Normalized Random Walk (C-H Zhang); Analysis of a Sequence of Dependent 2 x 2 Tables (S G Kou & Z Ying); A New Test of Symmetry about an Unknown Median (W Miao et al.); The Logistic Distribution and a Rank Test for Non-Transitivity (B M Brown et al.); and other papers.

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Book SynopsisThere have been major developments in the field of statistics over the last quarter century, spurred by the rapid advances in computing and data-measurement technologies. These developments have revolutionized the field and have greatly influenced research directions in theory and methodology. Increased computing power has spawned entirely new areas of research in computationally-intensive methods, allowing us to move away from narrowly applicable parametric techniques based on restrictive assumptions to much more flexible and realistic models and methods. These computational advances have also led to the extensive use of simulation and Monte Carlo techniques in statistical inference. All of these developments have, in turn, stimulated new research in theoretical statistics.This volume provides an up-to-date overview of recent advances in statistical modeling and inference. Written by renowned researchers from across the world, it discusses flexible models, semi-parametric methods and transformation models, nonparametric regression and mixture models, survival and reliability analysis, and re-sampling techniques. With its coverage of methodology and theory as well as applications, the book is an essential reference for researchers, graduate students, and practitioners.Table of ContentsStatistics and Soccer; Survival Analysis; Reliability Techniques; Semiparametric Methods; Transformation Models; Nonparametric Regression; Clustering and Mixture Models; Bayesian Nonparametric Inference; Rank-Based Methods; Monte Carlo and Resampling Methods; Constrained Inference.

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Book SynopsisThis textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail.Table of ContentsThe Need for Measure Theory; Probability Triples; Further Probabilistic Foundations; Expected Values; Inequalities and Convergence; Distributions of Random Variables; Stochastic Processes and Gambling Games; Discrete Markov Chains; More Probability Theorems; Weak Convergence; Characteristic Functions; Decomposition of Probability Laws; Conditional Probability and Expectation; Martingales; General Stochastic Processes.

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Book SynopsisThe first edition of this classic book has become the authoritative reference for physicists desiring to master the finer points of statistical data analysis. This second edition contains all the important material of the first, much of it unavailable from any other sources. In addition, many chapters have been updated with considerable new material, especially in areas concerning the theory and practice of confidence intervals, including the important Feldman-Cousins method. Both frequentist and Bayesian methodologies are presented, with a strong emphasis on techniques useful to physicists and other scientists in the interpretation of experimental data and comparison with scientific theories. This is a valuable textbook for advanced graduate students in the physical sciences as well as a reference for active researchers.Trade Review"I highly recommend that this book be kept on every desk -- for consultation when a question arises, for browsing when in the mood to learn something interesting, and for a straight read-though to get a grounding in the classical theory of statistics from an experimental physicist's perspective."CERN CourierTable of ContentsBasic Concepts in Probability; Convergence and the Law of Large Numbers; Probability Distributions; Information; Decision Theory; Theory of Estimators; Point Estimation in Practice; Interval Estimation; Test of Hypotheses; Goodness-of-Fit Tests.

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Book SynopsisThis textbook presents a classical approach to some techniques of multivariate analysis in a simple and transparent manner. It offers clear and concise development of the concepts; interpretation of the output of the analysis; and criteria for selection of the methods, taking into account the strengths and weaknesses of each. With its roots in matrix algebra, for which a separate chapter has been added as an appendix, the book includes both data-oriented techniques and a reasonable coverage of classical methods supplemented by comments about robustness and general practical applicability. It also illustrates the methods of numerical calculations at various stages.This self-contained book is ideal as an advanced textbook for graduate students in statistics and other disciplines like social, biological and physical sciences. It will also be of benefit to professional statisticians.The author is a former Professor of the Indian Statistical Institute, India.Table of ContentsOrganization of the Multivariate Data, Measures of Distance, Treatment of Missing Observations; Multivariate Normal Distribution and Related Distributions (Wishart, Hotelling's T2, Wilks'); Tests for Multivariate Normality, Robust Estimation of Location and Scale Parameters; Testing of Multivariate Hypotheses, Simultaneous Confidence Intervals; Multivariate Regression Analysis; Analysis of Variance and Covariance; Principal Component Analysis; Factor Analysis; Canonical Correlation; Classification and Discrimination.

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Book SynopsisThis book presents up-to-date theory and methods of statistical hypothesis testing based on measure theory. The so-called statistical space is a measurable space adding a family of probability measures. Most topics in the book will be developed based on this term. The book includes some typical data sets, such as the relation between race and the death penalty verdict, the behavior of food intake of two kinds of Zucker rats, and the per capita income and expenditure in China during the 1978-2002 period. Emphasis is given to the process of finding appropriate statistical techniques and methods of evaluating these techniques.Table of ContentsStatistical Spaces; Methods of Statistical Tests; The Comparison of Test Statistics; Parametric Tests for Simple Models; Parametric Tests for Regression Models.

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Book SynopsisThis monograph presents a comprehensive and up-to-date account of the developments in optimality aspects of crossover designs. Crossover designs are immensely useful in various areas of human investigation including agriculture, animal nutrition, clinical trials, pharmaceutical studies, biological assays, weather modification experiments, sensory evaluation of food products and learning experiments. Research on the optimality aspects of crossover designs has developed only in the last three decades, and it has now emerged as a potential field for further investigation. This book is the first comprehensive treatise on this subject. It covers optimal crossover designs at length by consolidating vast amounts of material from the literature, and includes many recent and deep results. It is expected that this book will not only provide a one-stop reference for the available results, but also encourage further research in this area of substantial practical relevance.Table of ContentsIntroduction; Optimality of Balanced and Strongly Balanced Designs; Some Optimal Designs with p < t; Optimal Designs via Approximate Theory; Optimality Under Other Additive Models; Optimality Under Nonadditive Models; Further Developments.

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Book SynopsisThis volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the methods and techniques described in the book. It covers the fundamental theories in linear regression analysis and is extremely useful for future research in this area. The examples of regression analysis using the Statistical Application System (SAS) are also included. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject fields.Table of ContentsIntroduction; Simple Linear Regression; Multiple Linear Regression; Detection of Outliers and Influential Observations in Multiple Linear Regression; Model Selection in Linear Regression; Linear Regression for Models with Heterogeneous Error; Regression Model for Discrete Response Variables; Variable Transformation in Linear Regression.

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Book SynopsisArthur Lyon Bowley, the founding father of modern statistics, was an important and colorful figure and a leader in cementing the foundations of statistical methodology, including survey methodology, and of the applications of statistics to economical and social issues during the late 19th and early 20th centuries. In many respects, he was ahead of his time.The giants in this field around that time were largely concentrated in the British Isles and Scandinavian countries; among these contributors, Arthur Bowley was one of the most active in revolutionizing statistical methodology and its economic applications. However, Bowley has been vastly undervalued by subsequent commentators — while hundreds of articles and books have been written on Karl Pearson, those on Arthur Bowley amount to a dozen or less. This book seeks to remedy this and fill in an important omission in the monographical literature on the history of statistics. In particular, the recent resurgence of interest in poverty research has led to a renewed interest in Bowley's legacy.Table of ContentsBiography and Scientific Activities of A L Bowley; Statistical Papers and Books; Economic Papers and Books; A L Bowley's Everlasting Effect.

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Book SynopsisExplanation of the basic concepts and methods of statistics requires a reasonably good mathematical background, at least at a first-year-level knowledge of calculus. Most of the statistical software explain how to conduct data analysis, but do not explain when to apply and when not to apply it. Keeping this in view, we try to explain the basic concepts of probability and statistics for students with an understanding of a first course in calculus at the undergraduate level.Designed as a textbook for undergraduate and first-year graduate students in statistics, bio-statistics, social sciences and business administration programs as well as undergraduates in engineering sciences and computer science programs, it provides a clear exposition of the theory of probability along with applications in statistics. The book contains a large number of solved examples and chapter-end exercises designed to reinforce the probability theory and emphasize statistical applications.Table of ContentsProbability, Conditional Probability, Independence; Discrete Probability Distributions, Probability Generating Function; Distribution Function, Probability Density Function, Expectation and Variance, Moments, Moment Generating Function, Functions of a Random Variable, Standard Continuous Probability Distributions; Bivariate Probability Distributions, Conditional Distributions, Independence, Expectation of a Function of a Random Vector, Correlation and Regression, Moment Generating Function, Multivariate Probability Distributions; Functions of Two Random Variables, Functions of Multivariate Random Vectors, Sampling Distributions, Chebyshev's Inequality, Weak Law of Large Numbers, Poisson Approximation to a Binomial Distribution, Central Limit Theorem, Normal Approximation to a Binomial Distribution, Approximation to a Chi-Square Distribution by a Normal Distribution, Convergence of Sequences of Random Variables; Methods of Estimation, Cramer-Rao Inequality, Efficient Estimation, Sufficient Statistics, Properties of a Maximum Likelihood Estimator, Bayes Estimation, Estimation of a Probability Density Function; Interval Estimation (Confidence Intervals), Testing of Hypotheses, Chi-Square Tests; Simple Linear Regression Model, Multiple Linear Regression Model, Correlation.

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Book SynopsisThis book provides the mathematical definition of white noise and gives its significance. White noise is in fact a typical class of idealized elemental (infinitesimal) random variables. Thus, we are naturally led to have functionals of such elemental random variables that is white noise. This book analyzes those functionals of white noise, particularly the generalized ones called Hida distributions, and highlights some interesting future directions. The main part of the book involves infinite dimensional differential and integral calculus based on the variable which is white noise.The present book can be used as a supplementary book to Lectures on White Noise Functionals published in 2008, with detailed background provided.Table of ContentsWhite Noise and Its Probability Distribution; Linear Functionals of White Noise; Gaussian Systems and Their Representations; Nonlinear Functionals of White Noise; Hida Distributions (Generalized Functionals of White Noise); Applications to Quantum Dynamics, Statistics and Biology.

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Book SynopsisThis volume contains a collection of research articles on multivariate statistical methods, encompassing both theoretical advances and emerging applications in a variety of scientific disciplines. It serves as a tribute to Professor S N Roy, an eminent statistician who has made seminal contributions to the area of multivariate statistical methods, on his birth centenary. In the area of emerging applications, the topics include bioinformatics, categorical data and clinical trials, econometrics, longitudinal data analysis, microarray data analysis, sample surveys, statistical process control, etc.Researchers, professionals and advanced graduates will find the book an essential resource for modern developments in theory as well as for innovative and emerging important applications in the area of multivariate statistical methods.Table of ContentsHigh-Dimensional Discrete Statistical Models; Multivariate Theory for High-Dimensional Data with Fewer Observations; Model-based Penalized Clustering for Multivariate Data; Jacobians under Constraints and Statistical Bioinformatics; Cluster Validation for Microarray Data; Flexible Bivariate Circular Models; Optimal Text Space Representation Through Circular Data Analysis; Linear Regression for Random Measures; Mixed Multivariate Models for Random Sums and Maxima; Estimation of the Box-Cox Transformation Parameters; Generation of Multivariate Densities; Smooth Estimation of Multivariate Distribution and Density and Functions; Estimation Using Quantile Function Structure; Optimal Estimating Functions in the Presence of Nuisance Parameters; Inference in Exponential Family Regression Models Under Shape Constraints; Optimal Adaptive Rule in Testing Problem; Robust Tests for Inverse Gaussian Scale Parameters; Clusterwise Regression Using Dirichlet Mixtures; Bayesian Analysis of Rank Data; Bayesian Tests of Equality of Stratified Proportions for a Multiple-Response Categorical Variable; Respondent-Generated Intervals in Sample Surveys; Quality Index and Mahalanobis D2 Statistic; AQL-based Multiattribute Sampling Scheme; Multivariate Quality Management; Large Time Series of Categorical Data; Estimation of Integrated Covolatility for Asynchronous Assets; Improving the Hansen-Hurwitz Estimator in PPSWR Sampling.

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Book SynopsisIn China, lots of excellent students who are good at maths take an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year.The author is one of the senior coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. This book will, in an interesting problem-solving way, explain what probability theory is: its concepts, methods and meanings; particularly, two important concepts — probability and mathematical expectation (briefly expectation) — are emphasized. It consists of 65 problems, appended by 107 exercises and their answers.

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Book Synopsis'Written by a well-known expert in fractional stochastic calculus, this book offers a comprehensive overview of Gaussian analysis, with particular emphasis on nonlinear Gaussian functionals. In addition, it covers some topics that are not frequently encountered in other treatments, such as Littlewood-Paley-Stein, etc. This coverage makes the book a valuable addition to the literature. Many results presented in this book were hitherto available only in the research literature in the form of research papers by the author and his co-authors.'Mathematical Reviews ClippingsAnalysis of functions on the finite dimensional Euclidean space with respect to the Lebesgue measure is fundamental in mathematics. The extension to infinite dimension is a great challenge due to the lack of Lebesgue measure on infinite dimensional space. Instead the most popular measure used in infinite dimensional space is the Gaussian measure, which has been unified under the terminology of 'abstract Wiener space'.Out of the large amount of work on this topic, this book presents some fundamental results plus recent progress. We shall present some results on the Gaussian space itself such as the Brunn-Minkowski inequality, Small ball estimates, large tail estimates. The majority part of this book is devoted to the analysis of nonlinear functions on the Gaussian space. Derivative, Sobolev spaces are introduced, while the famous Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood-Paley-Stein-Meyer theory are given in details.This book includes some basic material that cannot be found elsewhere that the author believes should be an integral part of the subject. For example, the book includes some interesting and important inequalities, the Littlewood-Paley-Stein-Meyer theory, and the Hörmander theorem. The book also includes some recent progress achieved by the author and collaborators on density convergence, numerical solutions, local times.

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Book SynopsisThe book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of many new results are presented in great detail. Original tools are developed for spatial point processes and stochastic integration with respect to local martingales in the plane.This second edition covers properties of random variables and time continuous local martingales with a discontinuous predictable compensator, with exponential inequalities and new inequalities for their maximum variable and their p-variations. A chapter on stochastic calculus presents the exponential sub-martingales developed for stationary processes and their properties. Another chapter devoted itself to the renewal theory of processes and to semi-Markovian processes, branching processes and shock processes. The Chapman-Kolmogorov equations for strong semi-Markovian processes provide equations for their hitting times in a functional setting which extends the exponential properties of the Markovian processes.

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Book Synopsis'The book provides a comprehensive review of the DRM approach to data fusion. It is well written and easy to follow, although the technical details are not trivial. The authors did an excellent job in making a concise introduction of the statistical techniques in data fusion. The book contains several real data … Overall, I found that the book covers an important topic and the DRM is a promising tool in this area. Researchers on data fusion will surely find this book very helpful and I will use this book in studying with my PhD students.'Journal of the American Statistical AssociationThis book comes up with estimates or decisions based on multiple data sources as opposed to more narrowly defined estimates or decisions based on single data sources. And as the world is awash with data obtained from numerous and varied processes, there is a need for appropriate statistical methods which in general produce improved inference by multiple data sources.The book contains numerous examples useful to practitioners from genomics. Topics range from sensors (radars), to small area estimation of body mass, to the estimation of small tail probabilities, to predictive distributions in time series analysis.

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Book SynopsisWritten by renowned experts in the field, this reissue of a textbook has as its unifying theme the role that probability models have had, and continue to have, in scientific and practical applications. It includes many examples, with actual data, of real-world use of probability models, while expositing the mathematical theory of probability at an introductory calculus-based level. Detailed descriptions of the properties and applications of probability models that have successfully modeled real phenomena are given, as well as an explanation of methods for testing goodness of fit of these models. Readers will receive a firm foundation in techniques for deriving distributions of various summaries of data that will prepare them for subsequent studies of statistics, as well as a solid grounding in concepts such as that of conditional probability that will prepare them for more advanced courses in stochastic processes.

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Book SynopsisThe book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber-Shiu functions and dependence.

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Book SynopsisThis book showcases the innovative research of Professor Skovgaard, by providing in one place a selection of his most important and influential papers. Introductions by colleagues set in context the highlights, key achievements, and impact, of each work.This book provides a survey of the field of asymptotic theory and inference as it was being pushed forward during an exceptionally fruitful time. It provides students and researchers with an overview of many aspects of the field.

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Book SynopsisThis textbook introduces the basic concepts from probability theory and statistics which are needed for statistical analysis of data encountered in the biological and health sciences. No previous study is required. Advanced mathematical tools, such as integration and differentiation, are kept to a minimum. The emphasis is put on the examples. Probabilistic methods are discussed at length, but the focus of this edition is on statistics.The examples are kept simple, so that the reader can learn quickly and see the usefulness of various statistical and probabilistic methods. Some of the examples used in this book draw attention to various problems related to environmental issues, climate change, loss of bio-diversity, and their impact on wildlife and humans.In comparison with the first edition of the book, this second edition contains additional topics such as power, sample size computation and non-parametric methods, and includes a large collection of new problems, as well as the answers to odd-numbered problems. Several sections of this edition are accompanied by instructions using the programming language R for statistical computing and graphics.The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to sales@wspc.com.

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Book Synopsis'Heavy-tailed risk modelling plays a central role in modern risk theory; within this perspective, the book provides an excellent guide concerning problems and solutions in risk theory.'zbMATHThis book is written to help graduate students and young researchers to enter quickly into the subject of Risk Theory. It can also be used by actuaries and financial practitioners for the optimization of their decisions and further by regulatory authorities for the stabilization of the insurance industry. The topic of extreme claims is especially presented as a crucial feature of the modern ruin probability.

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Book SynopsisThis is a book of elementary probability theory that includes a chapter on algorithmic randomness. It rigorously presents definitions and theorems in computation theory, and explains the meanings of the theorems by comparing them with mechanisms of the computer, which is very effective in the current computer age.Random number topics have not been treated by any books on probability theory, only some books on computation theory. However, the notion of random number is necessary for understanding the essential relation between probability and randomness. The field of probability has changed very much, thus this book will make and leave a big impact even to expert probabilists.Readers from applied sciences will benefit from this book because it presents a very proper foundation of the Monte Carlo method with practical solutions, keeping the technical level no higher than 1st year university calculus.

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Book SynopsisExotic Betting at the Racetrack is unique as it covers the efficient-inefficient strategy to price and find profitable racetrack bets, along with handicapping that provides actual bets made by the author on essentially all of the major wagers offered at US racetracks. The book starts with efficiency, accuracy of the win odds, arbitrage, and optimal betting strategies. Examples and actual bets are shown for various wagers including win, place and show, exacta, quinella, double, trifecta, superfecta, Pick 3, 4 and 6 and rainbow pick 5 and 6. There are discussions of major races including the Breeders' Cup, Pegasus, Dubai World Cup and the US Triple Crown from 2012-2018. Dosage analysis is also described and used. An additional feature concerns great horses such as the great mares Rachel Alexandra, Zenyatta, Goldikova, Treve, Beholder and Song Bird. There is a discussion of horse ownership and a tour through arguably the world's top trainer Frederico Tesio and his stables and horses in Italy.Related Link(s)

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Book SynopsisRandom matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists.In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, the subject has seen applications in such diverse areas as large dimensional data analysis and wireless communications.This volume contains chapters written by the leading participants in the field which will serve as a valuable introduction into this very exciting area of research.Table of ContentsThe Stieltjes Transform and Its Role in Eigenvalue Behavior of Large Dimensional Random Matrices (J W Silverstein); Beta Random Matrix Ensembles (P Forrester); Future of Statistics (Z Bai);  and Shannon Transforms: A Bridge between Random Matrices and Wireless Communications (A M Tulino); The Replica Method in Multiuser Communications (R R Muller).

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Book SynopsisThis book presents a collection of invited articles by distinguished probabilists and statisticians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute — a notable institute with significant achievement in research areas of statistics, probability and mathematics — in 2007.With a wide coverage of topics in probability and statistics, the articles provide a current perspective of different areas of research, emphasizing the major challenging issues. The book also proves its reference and utility value for practitioners as the articles in Statistics contain applications of the methodology that will be of use to practitioners. To professional statisticians and mathematicians, this is a unique volume for its illuminating perspectives on several important aspects of probability and statistics.Table of ContentsEntropy and Martingale (K B Athreya & M G Nadkarni); Marginal Quantiles: Asymptotics for Functions of Order Statistics (J Babu); Statistics on Manifolds with Applications to Shape Spaces (R Bhattacharya & A Bhattacharya); Reinforcement Learning - A Bridge Between Numerical Methods and Monte Carlo (V S Borkar); Bayesian Nonparametric Approach to Multiple Testing (S Ghosal & A Roy); Higher Criticism in the Context of Unknown Distribution, Non-Independence and Classification (P Hall); Bayesian Inference on Mixtures of Distributions (K Lee et al.); Markov Processes Generated by Random Iterates of Monotone Maps: Theory and Applications (M Majumdar); An Invitation to Quantum Information Theory (K R Parthasarathy); On the Classification of Binary Shifts on the Hyperfinite II1 Factor (G L Price); Scaling Limit (S R S Varadhan).

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Book SynopsisIn this monograph, the author presents univariate and multivariate probabilistic inequalities with coverage on basic probabilistic entities like expectation, variance, moment generating function and covariance. These are built on the recent classical form of real analysis inequalities which are also discussed in full details. This treatise is the culmination and crystallization of the author's last two decades of research work in related discipline. Each of the chapters is self-contained and a few advanced courses can be taught out of this book. Extensive background and motivations for specific topics are given in each chapter. A very extensive list of references is also provided at the end.The topics covered in this unique book are wide-ranging and diverse. The opening chapters examine the probabilistic Ostrowski type inequalities, and various related ones, as well as the largely discusses about the Grothendieck type probabilistic inequalities. The book is also about inequalities in information theory and the Csiszar's f-Divergence between probability measures. A great section of the book is also devoted to the applications in various directions of Geometry Moment Theory. Also, the development of the Grüss type and Chebyshev-Grüss type inequalities for Stieltjes integrals and the applications in probability are explored in detail. The final chapters discuss the important real analysis methods with potential applications to stochastics. The book will be of interest to researchers and graduate students, and it is also seen as an invaluable reference book to be acquired by all science libraries as well as seminars that conduct discussions on related topics.Table of ContentsBasic Stochastic Ostrowski Inequalities; General Probabilistic Inequalities; Optimal Estimation of Discrete Csiszar f-Divergence; Holder-Like Csiszar's f-Divergence Inequalities; Prokhorov Radius Around Zero Using Three Moment Constraints; Precise Rates of Prokhorov Convergence Using Three Moment Conditions; Discrepancies Between General Integral Means; An Expansion Formula; and other chapters.

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Book SynopsisThe book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation — the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups — is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm-Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.Table of ContentsProbability Measures on Metric Spaces; The Fourier Transform in a Banach Space; The Structure of Infinitely Divisible Probability Measures; Harmonic Analysis of Convolution Semigroups; Negative Definite Functions and Convolution Semigroups; Probabilistic Properties of Convolution Semigroups; Hypergroups in Probability Theory; Limit Theorems on Locally Compact Abelian Groups.

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Book SynopsisThe book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber-Shiu functions and dependence.Table of ContentsIntroduction; Some General Tools and Results; The Compound Poisson Model; The Probability of Ruin within Finite Time; Renewal Arrivals; Risk Theory in a Markovian Environment; Premiums Depending on the Current Reserve; Matrix-Analytic Methods; Ruin Probabilities in the Presence of Heavy Tails; Simulation Methodology; Miscellaneous Topics; Stochastic Control; Gerber-Shiu Functions; Recent Developments in Monte Carlo Methods; Recent Developments in Fluctuation Theory for Levy Processes; Payment of Dividends; Tail Estimation; Dependent Risks; Level-Dependent Risk Processes.

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Book SynopsisStatistical reasoning and modeling are of critical importance to modern biology. This textbook introduces fundamental concepts from probability and statistics which will pave the way for the student of biology to become a well-rounded scientist. No previous study of probability or statistics is assumed. Calculus topics are not used extensively in this book, though some integration and differentiation are expected. The calculus prerequisite is primarily intended to assure a certain level of mathematical maturity. This book puts emphasis on examples, which are presented to motivate the theory. The presentation style is concise and self-contained, briefly including the mathematical elements that are needed for studying probability and statistics. The examples are relevant to students in the life sciences with interests in genetics, biology, ecology, health, etc. We believe that aspects of probability theory are of biological interest and that probability underlies the theory of inferential statistics. Thus, we place an equal emphasis on probability and statistics which are both essential for solving and understanding many types of biological problems.Table of ContentsProbability: Probability; Combinatorial Techniques; Elementary Genetics; Conditional Probability; Bayes' Rule; Statistical Independence; Discrete and Continuous Random Variables; Binomial; Poisson; Normal Distributions; Statistics: Gathering and Describing Data; Sampling Distributions; Point and Interval Estimation; Hypothesis Testing; Comparison of Two Independent Samples; Paired Samples; Categorical Data, Regression and Correlation.

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Book SynopsisThis textbook contains a consideration of the wide field of problems connected with statistical methods of processing of observed data, with the main examples and considered models related to geophysics and seismic exploration. This textbook will be particularly helpful to students and professionals from various fields of physics, connected with an estimation of the parameters of the physical objects by experimental data. The reader can also find many important topics, which are the basis for statistical methods of estimation and inverse problem solutions.Table of ContentsBasic Concepts of the Probability Theory; Elements of Mathematical Statistics; Models of Measurement Data; The Relationships of Sounding Signal and Medium Parameters; Ray Theory of Wave Propagation; Methods for Parameter Estimation; Statistical Criteria for Choice of Model; Algorithms of Approximation of Geophysical Data; Elements of Applied Functional Analysis; Construction of Tomographic Functionals; Tomography Methods of recovering the Image of Medium; Methods of Transforms and Data Analysis.

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Book SynopsisThis is the proceedings of the 29th Conference on Quantum Probability and Infinite Dimensional Analysis, which was held in Hammamet, Tunisia.Table of ContentsHeisenberg Algebras; Multiplicative Renormalization for Power Functions, Quadratic Exponential Vectors; Kolmogorovian Models for Epr-Experiment; Markov Processes; Quantum Stochastic Processes; White Noise Analysis; CAR Algebras; Differential Equations for White Noise Operators; Gibbs Conditioning Principle; Quantum Fokker-Planck Models; Levy-Meixner Oscillator Algebra; Quantum Gross Laplacian; Levy Models in Mathematical Finance;

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Book SynopsisThis book is a collaborative effort from three workshops held over the last three years, all involving principal contributors to the vine-copula methodology. Research and applications in vines have been growing rapidly and there is now a growing need to collate basic results, and standardize terminology and methods. Specifically, this handbook will (1) trace historical developments, standardizing notation and terminology, (2) summarize results on bivariate copulae, (3) summarize results for regular vines, and (4) give an overview of its applications. In addition, many of these results are new and not readily available in any existing journals. New research directions are also discussed.Table of ContentsIntroduction; Multivariate Copulae; Vine Copulae; Sampling Count Variables; Micro Correlations and Tail Dependence; Copula Information Criterion; Dependence Comparisons of Vine Copulae; Tail Dependence in Vine Copulae; Counting Vines; Optimal Truncation of Vines; Non-Parametric BBNs vs. Vines; Joint Bayesian Inference of D-Vines with AR(1) Margins; Modeling Dependence Between Financial Returns Using PCC; Dynamic D-Vine Model; Regular Vines: Generation Algorithm and Number of Equivalent Classes;

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Book SynopsisThis book provides a comprehensive account of stochastic filtering as a modeling tool in finance and economics. It aims to present this very important tool with a view to making it more popular among researchers in the disciplines of finance and economics. It is not intended to give a complete mathematical treatment of different stochastic filtering approaches, but rather to describe them in simple terms and illustrate their application with real historical data for problems normally encountered in these disciplines. Beyond laying out the steps to be implemented, the steps are demonstrated in the context of different market segments. Although no prior knowledge in this area is required, the reader is expected to have knowledge of probability theory as well as a general mathematical aptitude.Its simple presentation of complex algorithms required to solve modeling problems in increasingly sophisticated financial markets makes this book particularly valuable as a reference for graduate students and researchers interested in the field. Furthermore, it analyses the model estimation results in the context of the market and contrasts these with contemporary research publications. It is also suitable for use as a text for graduate level courses on stochastic modeling.Table of ContentsIntroduction to the Background of the Stochastic Filtering Problems; Filtering the Forward Exchange Rate Risk Premium; Inferring Unit Price of Risk in the Equity Market; Components of Inflation Uncertainty; Estimating Non-Markovian Interest Rate Model from Bond Prices; Filtering Application in Interest Rate Futures Prices; Multifactor Model of Time Series Dynamics of Credit Spread for Different Rating Classes; Short-Term and Long-Term Dynamics of Credit Default Swaps; Implied Volatility in Options on Credit Default Swaps; Non-Linear Filtering in Stochastic Variance Model for Interest Rates; Filtering Problems with Jumps.

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Book SynopsisThis book provides a basic grounding in the use of probability to model random financial phenomena of uncertainty, and is targeted at an advanced undergraduate and graduate level. It should appeal to finance students looking for a firm theoretical guide to the deep end of derivatives and investments. Bankers and finance professionals in the fields of investments, derivatives, and risk management should also find the book useful in bringing probability and finance together.The book contains applications of both discrete time theory and continuous time mathematics, and is extensive in scope. Distribution theory, conditional probability, and conditional expectation are covered comprehensively, and applications to modeling state space securities under market equilibrium are made. Martingale is studied, leading to consideration of equivalent martingale measures, fundamental theorems of asset pricing, change of numeraire and discounting, risk-adjusted and forward-neutral measures, minimal and maximal prices of contingent claims, Markovian models, and the existence of martingale measures preserving the Markov property. Discrete stochastic calculus and multiperiod models leading to no-arbitrage pricing of contingent claims are also to be found in this book, as well as the theory of Markov Chains and appropriate applications in credit modeling. Measure-theoretic probability, moments, characteristic functions, inequalities, and central limit theorems are examined. The theory of risk aversion and utility, and ideas of risk premia are considered. Other application topics include optimal consumption and investment problems and interest rate theory.Table of ContentsMeasure-Theoretic Probability; Moments; Characteristic Functions; Inequalities; Central Limit Theorem; Distribution Theory; Conditional Probability; Conditional Expectation; State Space Securities; Market Equilibrium; Martingales; Equivalent Martingale Measures; Fundamental Theorems of Asset Pricing; Change of Numeraire; Risk-Adjusted and Forward-Neutral Measures; Minimal and Maximal Prices of Contingent Claims; Markovian Models; Stochastic Calculus; No-Arbitrage Pricing of Contingent Claims; Utility Theory; Theory of Risk Aversion; Risk Premia; Theory of Markov Chains; Credit Modeling; Optimal Consumption and Investment; Multi-Period Models; Interest Rate Theory.

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Book SynopsisThe Theory of Probability is a major tool that can be used to explain and understand the various phenomena in different natural, physical and social sciences. This book provides a systematic exposition of the theory in a setting which contains a balanced mixture of the classical approach and the modern day axiomatic approach. After reviewing the basis of the theory, the book considers univariate distributions, bivariate normal distribution, multinomial distribution, convergence of random variables and elements of stochastic process. Difficult ideas have been explained lucidly and augmented with explanatory notes, examples and exercises. The basic requirement for reading the book is the knowledge of mathematics at graduate level.This book tries to explain the difficult ideas in axiomatic approach to the theory in a clear and comprehensive manner. It addresses several unusual distributions including the power series distribution. Readers will find many worked-out examples and exercises with hints, which will make the book easily readable and engaging.The author is a former professor of the Indian Statistical Institute, India.Table of ContentsClassical Theory and Its Limitations; Axiomatic Approach; Random Variables and Distributions; Expectation of a Discrete Random Variable; Properties of Probability Distributions in R1; Generating Functions; Some Discrete Distributions in R1; Some Continuous Distributions in R1; Probability Distributions in Rn; Probability Distribution of Functions of Random Variables; Convergence of a Sequence of Random Variables.

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Book SynopsisSample surveys is the most important branch of statistics. Without sample surveys there is no data, and without data there is no statistics. This book is the culmination of the lecture notes developed by the authors. The approach is theoretical in the sense that it gives mathematical proofs of the results in sample surveys. Intended as a textbook for a one-semester course for undergraduate seniors or first-year graduate students, a prerequisite basic knowledge of algebra, calculus, and statistical theory is required to master the techniques described in this book.Table of ContentsSimple Random Sampling; Sampling with Varying Probabilities of Selection; Stratified Sampling; Systematic Sampling; Ratio Method of Estimation; Regression Method of Estimation; Cluster Sampling; Sub-Sampling Two-Stage and Three-Stage Sampling; Double Sampling; Non-Sampling Errors.

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Book SynopsisThis book presents a systematic, rigorous and comprehensive account of the theory and applications of incomplete block designs. All major aspects of incomplete block designs are considered by consolidating vast amounts of material from the literature including the classical incomplete block designs, like the balanced incomplete block (BIB) and partially balanced incomplete block (PBIB) designs. Other developments like efficiency-balanced designs, nested designs, robust designs, C-designs and alpha designs are also discussed, along with more recent developments in incomplete block designs for special types of experiments, like biological assays, test-control experiments and diallel crosses, which are generally not covered in existing books. Results on the optimality aspects of various incomplete block designs are reviewed in a separate chapter, that also includes recent optimality results for test-control comparisons, parallel-line assays and diallel cross experiments.Table of ContentsIntroduction; Analysis and Properties of Block Designs; Balanced Designs; Partially Balanced Designs; More Incomplete Block Designs; Optimality Aspects of Block Designs.

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Book SynopsisRecent research in probability has been concerned with applications such as data mining and finance models. Some aspects of the foundations of probability theory have receded into the background. Yet, these aspects are very important and have to be brought back into prominence.Table of ContentsProbability Distributions; Characteristic Functions; Analytic Characteristic Functions; Infinitely Divisible Distributions; Self-Decomposable Distributions; Triangular Arrays.

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