This is the standard textbook for courses on probability and statistics, not substantially updated. While helping students to develop their problem-solving skills, the author motivates students with practical applications from various areas of ECE that demonstrate the relevance of probability theory to engineering practice. Included are chapter overviews, summaries, checklists of important terms, annotated references, and a wide selection of fully worked-out real-world examples. In this edition, the Computer Methods sections have been updated and substantially enhanced and new problems have been added.

Mathematical Statistics for Economics and Business, Second Edition, provides a comprehensive introduction to the principles of mathematical statistics which underpin statistical analyses in the fields of economics, business, and econometrics. The selection of topics in this textbook is designed to provide students with a conceptual foundation that will facilitate a substantial understanding of statistical applications in these subjects. This new edition has been updated throughout and now also includes a downloadable Student Answer Manual containing detailed solutions to half of the over 300 end-of-chapter problems. After introducing the concepts of probability, random variables, and probability density functions, the author develops the key concepts of mathematical statistics, most notably: expectation, sampling, asymptotics, and the main families of distributions. The latter half of the book is then devoted to the theories of estimation and hypothesis testing with associated examples and problems that indicate their wide applicability in economics and business. Features of the new edition include: a reorganization of topic flow and presentation to facilitate reading and understanding; inclusion of additional topics of relevance to statistics and econometric applications; a more streamlined and simple-to-understand notation for multiple integration and multiple summation over general sets or vector arguments; updated examples; new end-of-chapter problems; a solution manual for students; a comprehensive answer manual for instructors; and a theorem and definition map. This book has evolved from numerous graduate courses in mathematical statistics and econometrics taught by the author, and will be ideal for students beginning graduate study as well as for advanced undergraduates.

This book is intended as a text for graduate students and as a reference for workers in probability and statistics. The prerequisite is honest calculus. The material covered in Parts Two to Five inclusive requires about three to four semesters of graduate study. The introductory part may serve as a text for an undergraduate course in elementary probability theory. Numerous historical marks about results, methods, and the evolution of various fields are an intrinsic part of the text. About a third of the second volume is devoted to conditioning and properties of sequences of various types of dependence. The other two thirds are devoted to random functions; the last Part on Elements of random analysis is more sophisticated.

Appropriate for a one-semester course, this self-contained book is an introduction to nonparametric curve estimation theory. It may be used for teaching graduate students in statistics (in this case an intermediate statistical inference, on the level of the book by G. Casella and R. Berger (1990) "Statistical Inference", Brooks/Cole, is the prerequisite) as well as for diverse classes with students from other sciences including engineering, business, social, medical, and biology.

Fractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of fBm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of fBm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.

This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

Testing for a unit root is now an essential part of time series analysis. Indeed no time series study in economics, and other disciplines that use time series observations, can ignore the crucial issue of nonstationarity caused by a unit root. However, the literature on the topic is large and often technical, making it difficult to understand the key practical issues. This volume provides an accessible introduction and a critical overview of tests for a unit root in time series, with extensive practical examples and illustrations using simulation analysis. It presents the concepts that enable the reader to understand the theoretical background, and importance of ranA--dom walks and Brownian motion, to the development of unit root tests. The book also examines the latest developments and practical concerns in unit root testing. This book is indispensable reading for all interested in econometrics, time series econometrics, applied econometrics and applied statistics. It will also be of interest to other disciplines, such as geography, climate change and meteorology, which use time series of data.

This volume provides an overview of the field of Astrostatistics understood as the sub-discipline dedicated to the statistical analysis of astronomical data. It presents examples of the application of the various methodologies now available to current open issues in astronomical research. The technical aspects related to the scientific analysis of the upcoming petabyte-scale databases are emphasized given the importance that scalable Knowledge Discovery techniques will have for the full exploitation of these databases. Based on the 2011 Astrostatistics and Data Mining in Large Astronomical Databases conference and school, this volume gathers examples of the work by leading authors in the areas of Astrophysics and Statistics, including a significant contribution from the various teams that prepared for the processing and analysis of the Gaia data.

This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.

This book is the outcome of the CIMPA School on Statistical Methods and Applications in Insurance and Finance, held in Marrakech and Kelaat M'gouna (Morocco) in April 2013. It presents two lectures and seven refereed papers from the school, offering the reader important insights into key topics. The first of the lectures, by Frederic Viens, addresses risk management via hedging in discrete and continuous time, while the second, by Boualem Djehiche, reviews statistical estimation methods applied to life and disability insurance. The refereed papers offer diverse perspectives and extensive discussions on subjects including optimal control, financial modeling using stochastic differential equations, pricing and hedging of financial derivatives, and sensitivity analysis. Each chapter of the volume includes a comprehensive bibliography to promote further research.

Bayesian analyses have made important inroads in modern clinical research due, in part, to the incorporation of the traditional tools of noninformative priors as well as the modern innovations of adaptive randomization and predictive power. Presenting an introductory perspective to modern Bayesian procedures, Elementary Bayesian Biostatistics explores Bayesian principles and illustrates their application to healthcare research. Building on the basics of classic biostatistics and algebra, this easy-to-read book provides a clear overview of the subject. It focuses on the history and mathematical foundation of Bayesian procedures, before discussing their implementation in healthcare research from first principles. The author also elaborates on the current controversies between Bayesian and frequentist biostatisticians. The book concludes with recommendations for Bayesians to improve their standing in the clinical trials community. Calculus derivations are relegated to the appendices so as not to overly complicate the main text. As Bayesian methods gain more acceptance in healthcare, it is necessary for clinical scientists to understand Bayesian principles. Applying Bayesian analyses to modern healthcare research issues, this lucid introduction helps readers make the correct choices in the development of clinical research programs.

Intended as a textbook for students taking a first graduate course in the subject, as well as for the general reference of interested research workers, this text discusses, in a readable form, developments from recently published work on certain broad topics not otherwise easily accessible, such as robust inference and the use of the bootstrap in a multivariate setting. A minimum background expected of the reader would include at least two courses in mathematical statistics, and certainly some exposure to the calculus of several variables together with the descriptive geometry of linear algebra.

Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability in solving problems in modern society.

This textbook addresses postgraduate students in applied mathematics, probability, and statistics, as well as computer scientists, biologists, physicists and economists, who are seeking a rigorous introduction to applied stochastic processes. Pursuing a pedagogic approach, the content follows a path of increasing complexity, from the simplest random sequences to the advanced stochastic processes. Illustrations are provided from many applied fields, together with connections to ergodic theory, information theory, reliability and insurance. The main content is also complemented by a wealth of examples and exercises with solutions.

Markov decision process (MDP) models are widely used for modeling sequential decision-making problems that arise in engineering, economics, computer science, and the social sciences. Many real-world problems modeled by MDPs have huge state and/or action spaces, giving an opening to the curse of dimensionality and so making practical solution of the resulting models intractable. In other cases, the system of interest is too complex to allow explicit specification of some of the MDP model parameters, but simulation samples are readily available (e.g., for random transitions and costs). For these settings, various sampling and population-based algorithms have been developed to overcome the difficulties of computing an optimal solution in terms of a policy and/or value function. Specific approaches include adaptive sampling, evolutionary policy iteration, evolutionary random policy search, and model reference adaptive search.
This substantially enlarged new edition reflects the latest developments in novel algorithms and their underpinning theories, and presents an updated account of the topics that have emerged since the publication of the first edition. Includes:
innovative material on MDPs, both in constrained settings and with uncertain transition properties;
game-theoretic method for solving MDPs;
theories for developing roll-out based algorithms; and
details of approximation stochastic annealing, a population-based on-line simulation-based algorithm.
The self-contained approach of this book will appeal not only to researchers in MDPs, stochastic modeling, and control, and simulation but will be a valuable source of tuition and reference for students of control and operations research.

The standard approach of most introductory books for practical statistics is that readers first learn the minimum mathematical basics of statistics and rudimentary concepts of statistical methodology. They then are given examples of analyses of data obtained from natural and social phenomena so that they can grasp practical definitions of statistical methods. Finally they go on to acquaint themselves with statistical software for the PC and analyze similar data to expand and deepen their understanding of statistical methods.

This book, however, takes a slightly different approach, using simulation data instead of actual data to illustrate the functions of statistical methods. Also, R programs listed in the book help readers realize clearly how these methods work to bring intrinsic values of data to the surface. R is free software enabling users to handle vectors, matrices, data frames, and so on.

For example, when a statistical theory indicates that an event happens with a 5 % probability, readers can confirm the fact using R programs that this event actually occurs with roughly that probability, by handling data generated by pseudo-random numbers. Simulation gives readers populations with known backgrounds and the nature of the population can be adjusted easily. This feature of the simulation data helps provide a clear picture of statistical methods painlessly.

Most readers of introductory books of statistics for practical purposes do not like complex mathematical formulae, but they do not mind using a PC to produce various numbers and graphs by handling a huge variety of numbers. If they know the characteristics of these numbers beforehand, they treat them with ease. Struggling with actual data should come later. Conventional books on this topic frighten readers by presenting unidentified data to them indiscriminately. This book provides a new path to statistical concepts and practical skills in a readily accessible manner. "

S. Panchapakesan has made significant contributions to ranking and selection and has published in many other areas of statistics, including order statistics, reliability theory, stochastic inequalities, and inference. Written in his honor, the twenty invited articles in this volume reflect recent advances in these areas and form a tribute to Panchapakesan 's influence and impact on these areas.

Featuring theory, methods, applications, and extensive bibliographies with special emphasis on recent literature, this comprehensive reference work will serve researchers, practitioners, and graduate students in the statistical and applied mathematics communities.

This edited volume presents current research in biostatistics with emphasis on biopharmaceutical applications. Featuring contributions presented at the 2017 ICSA Applied Statistics Symposium held in Chicago, IL on June 25 to 28, 2017, this book explores timely topics that have a high potential impact on statistical methodology and future research in biostatistics and biopharmaceuticals. The theme of this conference was Statistics for a New Generation: Challenges and Opportunities, in recognition of the advent of a new generation of statisticians. The conference attracted statisticians working in academia, government, and industry; domestic and international statisticians. From the conference, the editors selected 28 high-quality presentations and invited the speakers to prepare full chapters for this book. These contributions are divided into four parts: Part I Biostatistical Methodology, Part II Statistical Genetics and Bioinformatics, Part III Regulatory Statistics, and Part IV Biopharmaceutical Research and Applications.Featuring contributions on topics such as statistics in genetics, bioinformatics, biostatistical methodology, and statistical computing, this book is beneficial to researchers, academics, practitioners and policy makers in biostatistics and biopharmaceuticals.

During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related areas. This commemorative volume, dedicated to Kallianpur on the occasion of his seventy-fifth birthday, will pay tribute to his multi-faceted achievements and to the deep insight and inspiration he has so graciously offered his students and colleagues throughout his career. Contributors to the volume: S. Aida, N. Asai, K. B. Athreya, R. N. Bhattacharya, A. Budhiraja, P. S. Chakraborty, P. Del Moral, R. Elliott, L. Gawarecki, D. Goswami, Y. Hu, J. Jacod, G. W. Johnson, L. Johnson, T. Koski, N. V. Krylov, I. Kubo, H.-H. Kuo, T. G. Kurtz, H. J. Kushner, V. Mandrekar, B. Margolius, R. Mikulevicius, I. Mitoma, H. Nagai, Y. Ogura, K. R. Parthasarathy, V. Perez-Abreu, E. Platen, B. V. Rao, B. Rozovskii, I. Shigekawa, K. B. Sinha, P. Sundar, M. Tomisaki, M. Tsuchiya, C. Tudor, W. A. Woycynski, J. Xiong

This book seeks to bridge the gap between the parlance, the models, and even the notations used by physicists and those used by mathematicians when it comes to the topic of probability and stochastic processes. The opening four chapters elucidate the basic concepts of probability, including probability spaces and measures, random variables, and limit theorems. Here, the focus is mainly on models and ideas rather than the mathematical tools. The discussion of limit theorems serves as a gateway to extensive coverage of the theory of stochastic processes, including, for example, stationarity and ergodicity, Poisson and Wiener processes and their trajectories, other Markov processes, jump-diffusion processes, stochastic calculus, and stochastic differential equations. All these conceptual tools then converge in a dynamical theory of Brownian motion that compares the Einstein-Smoluchowski and Ornstein-Uhlenbeck approaches, highlighting the most important ideas that finally led to a connection between the Schroedinger equation and diffusion processes along the lines of Nelson's stochastic mechanics. A series of appendices cover particular details and calculations, and offer concise treatments of particular thought-provoking topics.

Introduction to Environmental Data Science focuses on data science methods in the R language applied to environmental research, with sections on exploratory data analysis in R including data abstraction, transformation, and visualization; spatial data analysis in vector and raster models; statistics & modelling ranging from exploratory to modelling, considering confirmatory statistics and extending to machine learning models; time series analysis, focusing especially on carbon and micrometeorological flux; and communication. Introduction to Environmental Data Science. It is an ideal textbook to teach undergraduate to graduate level students in environmental science, environmental studies, geography, earth science, and biology, but can also serve as a reference for environmental professionals working in consulting, NGOs, and government agencies at the local, state, federal, and international levels. Features * Gives thorough consideration of the needs for environmental research in both spatial and temporal domains. * Features examples of applications involving field-collected data ranging from individual observations to data logging. * Includes examples also of applications involving government and NGO sources, ranging from satellite imagery to environmental data collected by regulators such as EPA. * Contains class-tested exercises in all chapters other than case studies. Solutions manual available for instructors. * All examples and exercises make use of a GitHub package for functions and especially data.

The number of innovative applications of randomization tests in various fields and recent developments in experimental design, significance testing, computing facilities, and randomization test algorithms have necessitated a new edition of Randomization Tests.

Updated, reorganized, and revised, the text emphasizes the irrelevance and implausibility of the random sampling assumption for the typical experiment in three completely rewritten chapters. It also discusses factorial designs and interactions and combines repeated-measures and randomized block designs in one chapter. The authors focus more attention on the practicality of N-of-1 randomization tests and the availability of user-friendly software to perform them. In addition, they provide an overview of free and commercial computer programs for all of the tests presented in the book.

Building on the previous editions that have served as standard textbooks for more than twenty-five years, Randomization Tests, Fourth Edition includes a CD-ROM of up-to-date randomization test programs that facilitate application of the tests to experimental data. This CD-ROM enables students to work out problems that have been added to the chapters and helps professors teach the basics of randomization tests and devise tasks for assignments and examinations.

Essentials of Monte Carlo Simulation focuses on the fundamentals of Monte Carlo methods using basic computer simulation techniques. The theories presented in this text deal with systems that are too complex to solve analytically. As a result, readers are given a system of interest and constructs using computer code, as well as algorithmic models to emulate how the system works internally. After the models are run several times, in a random sample way, the data for each output variable(s) of interest is analyzed by ordinary statistical methods. This book features 11 comprehensive chapters, and discusses such key topics as random number generators, multivariate random variates, and continuous random variates. Over 100 numerical examples are presented as part of the appendix to illustrate useful real world applications. The text also contains an easy to read presentation with minimal use of difficult mathematical concepts. Very little has been published in the area of computer Monte Carlo simulation methods, and this book will appeal to students and researchers in the fields of Mathematics and Statistics.

This handbook provides a comprehensive overview of Partial Least Squares (PLS) methods with specific reference to their use in marketing and with a discussion of the directions of current research and perspectives. It covers the broad area of PLS methods, from regression to structural equation modeling applications, software and interpretation of results. The handbook serves both as an introduction for those without prior knowledge of PLS and as a comprehensive reference for researchers and practitioners interested in the most recent advances in PLS methodology.