This book studies values and attitudes in the Gulf region. In light of global power shifts, the threatening collapse of internal security in the West, and uncertainty about the current leadership vacuum in world society, this book explores a future leading role of the Gulf countries in such institutions as the G-20 and the OECD. Based on rigorous analysis of macro-level data and opinion surveys with relevance for the Gulf region, it analyzes the global macro-factors shaping the Gulf's future at a time of the global COVID-19 crisis and depression and rising global tensions. Starting with an empirical time series analysis of the long cycles of global politics and economics, it highlights the implications for the Gulf region. Offering a multivariate analysis of civil society values in the Gulf, the author analyzes value changes and attitudes on antisemitism, political Islam, internal security, democracy, and other issues of Arab politics. The partially optimistic conclusions of the study testify to the underestimated and incipient maturity of the Gulf's civil society and strongly suggest that the Gulf's future is rather with the free societies of the West and not with a Neo-Ottoman Empire in whatever form."Exceptional in scope and right up-to-the-minute in coverage" Brian M Pollins, Associate, Professor Emeritus, The Ohio State University. "An outstanding and topical book by an astute scholar of the MENA region" Professor Hussein Solomon, Academic Head of Department, Political Studies and Governance, University of the Free State, South Africa. "The most comprehensive and insightful study on the subject to date" Manfred B. Steger, Professor of Sociology, University of Hawai'i at Manoa and Global Professorial Fellow, Western Sydney University.

This richly illustrated book describes statistical extreme value theory for the quantification of natural hazards, such as strong winds, floods and rainfall, and discusses an interdisciplinary approach to allow the theoretical methods to be applied. The approach consists of a number of steps: data selection and correction, non-stationary theory (to account for trends due to climate change), and selecting appropriate estimation techniques based on both decision-theoretic features (e.g., Bayesian theory), empirical robustness and a valid treatment of uncertainties. It also examines and critically reviews alternative approaches based on stochastic and dynamic numerical models, as well as recently emerging data analysis issues and presents large-scale, multidisciplinary, state-of-the-art case studies. Intended for all those with a basic knowledge of statistical methods interested in the quantification of natural hazards, the book is also a valuable resource for engineers conducting risk analyses in collaboration with scientists from other fields (such as hydrologists, meteorologists, climatologists).

Access to large data sets has led to a paradigm shift in the tourism research landscape. Big data is enabling a new form of knowledge gain, while at the same time shaking the epistemological foundations and requiring new methods and analysis approaches. It allows for interdisciplinary cooperation between computer sciences and social and economic sciences, and complements the traditional research approaches. This book provides a broad basis for the practical application of data science approaches such as machine learning, text mining, social network analysis, and many more, which are essential for interdisciplinary tourism research. Each method is presented in principle, viewed analytically, and its advantages and disadvantages are weighed up and typical fields of application are presented. The correct methodical application is presented with a "how-to" approach, together with code examples, allowing a wider reader base including researchers, practitioners, and students entering the field. The book is a very well-structured introduction to data science - not only in tourism - and its methodological foundations, accompanied by well-chosen practical cases. It underlines an important insight: data are only representations of reality, you need methodological skills and domain background to derive knowledge from them - Hannes Werthner, Vienna University of Technology Roman Egger has accomplished a difficult but necessary task: make clear how data science can practically support and foster travel and tourism research and applications. The book offers a well-taught collection of chapters giving a comprehensive and deep account of AI and data science for tourism - Francesco Ricci, Free University of Bozen-Bolzano This well-structured and easy-to-read book provides a comprehensive overview of data science in tourism. It contributes largely to the methodological repository beyond traditional methods. - Rob Law, University of Macau

This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.

In many statistical applications the scientists have to analyze the occurrence of observed clusters of events in time or space. The scientists are especially interested to determine whether an observed cluster of events has occurred by chance if it is assumed that the events are distributed independently and uniformly over time or space. Applications of scan statistics have been recorded in many areas of science and technology including: geology, geography, medicine, minefield detection, molecular biology, photography, quality control and reliability theory and radio-optics.

This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Levy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Federale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields of stochastic analysis and mathematical physics. Contributors: S. Albeverio M. Arnaudon V. Bally V. Barbu H. Bessaih Z. Brzezniak K. Burdzy A.B. Cruzeiro F. Flandoli A. Kohatsu-Higa S. Mazzucchi C. Mueller J. van Neerven M. Ondrejat S. Peszat M. Veraar L. Weis J.-C. Zambrini

This proceedings volume gathers selected, peer-reviewed papers presented at the 41st International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (QP41) that was virtually held at the United Arab Emirates University (UAEU) in Al Ain, Abu Dhabi, from March 28th to April 1st, 2021. The works cover recent developments in quantum probability and infinite dimensional analysis, with a special focus on applications to mathematical physics and quantum information theory. Covered topics include white noise theory, quantum field theory, quantum Markov processes, free probability, interacting Fock spaces, and more. By emphasizing the interconnection and interdependence of such research topics and their real-life applications, this reputed conference has set itself as a distinguished forum to communicate and discuss new findings in truly relevant aspects of theoretical and applied mathematics, notably in the field of mathematical physics, as well as an event of choice for the promotion of mathematical applications that address the most relevant problems found in industry. That makes this volume a suitable reading not only for researchers and graduate students with an interest in the field but for practitioners as well.

This book primarily aims to discuss emerging topics in statistical methods and to booster research, education, and training to advance statistical modeling on interval-censored survival data. Commonly collected from public health and biomedical research, among other sources, interval-censored survival data can easily be mistaken for typical right-censored survival data, which can result in erroneous statistical inference due to the complexity of this type of data. The book invites a group of internationally leading researchers to systematically discuss and explore the historical development of the associated methods and their computational implementations, as well as emerging topics related to interval-censored data. It covers a variety of topics, including univariate interval-censored data, multivariate interval-censored data, clustered interval-censored data, competing risk interval-censored data, data with interval-censored covariates, interval-censored data from electric medical records, and misclassified interval-censored data. Researchers, students, and practitioners can directly make use of the state-of-the-art methods covered in the book to tackle their problems in research, education, training and consultation.

The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers- The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics. The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular. Prof. Vladimir V. UCHAIKIN is a known Russian scientist and pedagogue, a Honored Worker of Russian High School, a member of the Russian Academy of Natural Sciences. He is the author of about three hundreds articles and more than a dozen books (mostly in Russian) in Cosmic ray physics, Mathematical physics, Levy stable statistics, Monte Carlo methods with applications to anomalous processes in complex systems of various levels: from quantum dots to the Milky Way galaxy.

This book focuses on the multi-omics big-data integration, the data-mining techniques and the cutting-edge omics researches in principles and applications for a deep understanding of Traditional Chinese Medicine (TCM) and diseases from the following aspects: (1) Basics about multi-omics data and analytical methods for TCM and diseases. (2) The needs of omics studies in TCM researches, and the basic background of omics research in TCM and disease. (3) Better understanding of the multi-omics big-data integration techniques. (4) Better understanding of the multi-omics big-data mining techniques, as well as with different applications, for most insights from these omics data for TCM and disease researches. (5) TCM preparation quality control for checking both prescribed and unexpected ingredients including biological and chemical ingredients. (6) TCM preparation source tracking. (7) TCM preparation network pharmacology analysis. (8) TCM analysis data resources, web services, and visualizations. (9) TCM geoherbalism examination and authentic TCM identification. Traditional Chinese Medicine has been in existence for several thousands of years, and only in recent tens of years have we realized that the researches on TCM could be profoundly boosted by the omics technologies. Devised as a book on TCM and disease researches in the omics age, this book has put the focus on data integration and data mining methods for multi-omics researches, which will be explained in detail and with supportive examples the "What", "Why" and "How" of omics on TCM related researches. It is an attempt to bridge the gap between TCM related multi-omics big data, and the data-mining techniques, for best practice of contemporary bioinformatics and in-depth insights on the TCM related questions.

More data has been produced in the 21st century than all of human history combined. Yet, are we making better decisions today than in the past? How many poor decisions result from the absence of data? The existence of an overwhelming amount of data has affected how we make decisions, but it has not necessarily improved how we make decisions. To make better decisions, people need good judgment based on data literacy-the ability to extract meaning from data. Including data in the decision-making process can bring considerable clarity in answering our questions. Nevertheless, human beings can become distracted, overwhelmed, and even confused in the presence of too much data. The book presents cautionary tales of what can happen when too much attention is spent on acquiring more data instead of understanding how to best use the data we already have. Data is not produced in a vacuum, and individuals who possess data literacy will understand the environment and incentives in the data-generating process. Readers of this book will learn what questions to ask, what data to pay attention to, and what pitfalls to avoid in order to make better decisions. They will also be less vulnerable to those who manipulate data for misleading purposes.

Now in its second edition, this textbook provides an applied and unified introduction to parametric, nonparametric and semiparametric regression that closes the gap between theory and application. The most important models and methods in regression are presented on a solid formal basis, and their appropriate application is shown through numerous examples and case studies. The most important definitions and statements are concisely summarized in boxes, and the underlying data sets and code are available online on the book's dedicated website. Availability of (user-friendly) software has been a major criterion for the methods selected and presented. The chapters address the classical linear model and its extensions, generalized linear models, categorical regression models, mixed models, nonparametric regression, structured additive regression, quantile regression and distributional regression models. Two appendices describe the required matrix algebra, as well as elements of probability calculus and statistical inference. In this substantially revised and updated new edition the overview on regression models has been extended, and now includes the relation between regression models and machine learning, additional details on statistical inference in structured additive regression models have been added and a completely reworked chapter augments the presentation of quantile regression with a comprehensive introduction to distributional regression models. Regularization approaches are now more extensively discussed in most chapters of the book. The book primarily targets an audience that includes students, teachers and practitioners in social, economic, and life sciences, as well as students and teachers in statistics programs, and mathematicians and computer scientists with interests in statistical modeling and data analysis. It is written at an intermediate mathematical level and assumes only knowledge of basic probability, calculus, matrix algebra and statistics.

Intangible, invisible and worth trillions, risk is everywhere. Its quantification and management are key to the success and failure of individuals, businesses and governments. Whether you're an interested observer or pursuing a career in risk, this book delves into the complex and multi-faceted work that actuaries undertake to quantify, manage and commodify risk-supporting our society and servicing a range of multi-billion-dollar industries. Starting at the most basic level, this book introduces key concepts in actuarial science, insurance and pensions. Through case studies, explanations and mathematical examples, it fosters an understanding of current industry practice. This book celebrates the long history of actuarial science and poses the problems facing actuaries in the future, exploring complex global risks including climate change, aging populations, healthcare models and pandemic epidemiology from an actuarial perspective. It gives practical advice for new and potential actuaries on how to identify an area of work to go into, how best to navigate (and pass!) actuarial exams and how to develop your skills post-qualification. A Risky Business illuminates how actuaries are central to society as we know it, revealing what they do and how they do it. It is the essential primer on actuarial science.

"A First Course in Machine Learning by Simon Rogers and Mark Girolami is the best introductory book for ML currently available. It combines rigor and precision with accessibility, starts from a detailed explanation of the basic foundations of Bayesian analysis in the simplest of settings, and goes all the way to the frontiers of the subject such as infinite mixture models, GPs, and MCMC." -Devdatt Dubhashi, Professor, Department of Computer Science and Engineering, Chalmers University, Sweden "This textbook manages to be easier to read than other comparable books in the subject while retaining all the rigorous treatment needed. The new chapters put it at the forefront of the field by covering topics that have become mainstream in machine learning over the last decade." -Daniel Barbara, George Mason University, Fairfax, Virginia, USA "The new edition of A First Course in Machine Learning by Rogers and Girolami is an excellent introduction to the use of statistical methods in machine learning. The book introduces concepts such as mathematical modeling, inference, and prediction, providing 'just in time' the essential background on linear algebra, calculus, and probability theory that the reader needs to understand these concepts." -Daniel Ortiz-Arroyo, Associate Professor, Aalborg University Esbjerg, Denmark "I was impressed by how closely the material aligns with the needs of an introductory course on machine learning, which is its greatest strength...Overall, this is a pragmatic and helpful book, which is well-aligned to the needs of an introductory course and one that I will be looking at for my own students in coming months." -David Clifton, University of Oxford, UK "The first edition of this book was already an excellent introductory text on machine learning for an advanced undergraduate or taught masters level course, or indeed for anybody who wants to learn about an interesting and important field of computer science. The additional chapters of advanced material on Gaussian process, MCMC and mixture modeling provide an ideal basis for practical projects, without disturbing the very clear and readable exposition of the basics contained in the first part of the book." -Gavin Cawley, Senior Lecturer, School of Computing Sciences, University of East Anglia, UK "This book could be used for junior/senior undergraduate students or first-year graduate students, as well as individuals who want to explore the field of machine learning...The book introduces not only the concepts but the underlying ideas on algorithm implementation from a critical thinking perspective." -Guangzhi Qu, Oakland University, Rochester, Michigan, USA

Based on a two-semester course aimed at illustrating various interactions of "pure mathematics" with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory, this text unifies three general topics of analysis and physics, which are as follows: the dimensional analysis of physical quantities, which contains various applications including Kolmogorov's model for turbulence; functions of very large number of variables and the principle of concentration along with the non-linear law of large numbers, the geometric meaning of the Gauss and Maxwell distributions, and the Kotelnikov-Shannon theorem; and, finally, classical thermodynamics and contact geometry, which covers two main principles of thermodynamics in the language of differential forms, contact distributions, the Frobenius theorem and the Carnot-Caratheodory metric. It includes problems, historical remarks, and Zorich's popular article, "Mathematics as language and method."

This text introduces upper division undergraduate/beginning graduate students in mathematics, finance, or economics, to the core topics of a beginning course in finance/financial engineering. Particular emphasis is placed on exploiting the power of the Monte Carlo method to illustrate and explore financial principles. Monte Carlo is the uniquely appropriate tool for modeling the random factors that drive financial markets and simulating their implications. The Monte Carlo method is introduced early and it is used in conjunction with the geometric Brownian motion model (GBM) to illustrate and analyze the topics covered in the remainder of the text. Placing focus on Monte Carlo methods allows for students to travel a short road from theory to practical applications. Coverage includes investment science, mean-variance portfolio theory, option pricing principles, exotic options, option trading strategies, jump diffusion and exponential Levy alternative models, and the Kelly criterion for maximizing investment growth. Novel features: inclusion of both portfolio theory and contingent claim analysis in a single text pricing methodology for exotic options expectation analysis of option trading strategies pricing models that transcend the Black-Scholes framework optimizing investment allocations concepts thoroughly explored through numerous simulation exercises numerous worked examples and illustrations The mathematical background required is a year and one-half course in calculus, matrix algebra covering solutions of linear systems, and a knowledge of probability including expectation, densities and the normal distribution. A refresher for these topics is presented in the Appendices. The programming background needed is how to code branching, loops and subroutines in some mathematical or general purpose language. The mathematical background required is a year and one-half course in calculus, matrix algebra covering solutions of linear systems, and a knowledge of probability including expectation, densities and the normal distribution. A refresher for these topics is presented in the Appendices. The programming background needed is how to code branching, loops and subroutines in some mathematical or general purpose language. Also by the author: (with F. Mendivil) Explorations in Monte Carlo, (c)2009, ISBN: 978-0-387-87836-2; (with J. Herod) Mathematical Biology: An Introduction with Maple and Matlab, Second edition, (c)2009, ISBN: 978-0-387-70983-3.

These volumes present a selection of Erich L. Lehmann's monumental contributions to Statistics. These works are multifaceted. His early work included fundamental contributions to hypothesis testing, theory of point estimation, and more generally to decision theory. His work in Nonparametric Statistics was groundbreaking. His fundamental contributions in this area include results that came to assuage the anxiety of statisticians that were skeptical of nonparametric methodologies, and his work on concepts of dependence has created a large literature.

The two volumes are divided into chapters of related works. Invited contributors have critiqued the papers in each chapter, and the reprinted group of papers follows each commentary. A complete bibliography that contains links to recorded talks by Erich Lehmann - and which are freely accessible to the public - and a list of Ph.D. students are also included. These volumes belong in every statistician's personal collection and are a required holding for any institutional library.

Recent books in the Wiley Series in Probability and Mathematical Statistics Editors Vic Barnett J. Stuart Hunter Adrian F.M. Smith Geoffrey S. Watson Ralph A. Bradley Joseph B. Kadane Stephen M. Stigler Nicholas I. Fisher David G. Kendall Jozef L. Teugels Optimal Design of Experiments Friedrich Pukelsheim, Universität Augsburg, Augsburg, Germany Optimal Design of Experiments presents the first complete theoretical development of optimal design for the linear model, a unified exposition that embraces a wide variety of design problems. It describes the statistical theory involved in designing experiments, and applies it to typical special cases. The design problems originating from statistics are solved using tools from linear algebra and convex analysis. The material is presented in a very clear, careful and organized way. Rather than assaulting traditional ways of thinking about optimal design, this book pulls together formerly separate entities to create a common framework for diverse design problems that share a common goal. Statisticians, mathematicians, engineers, and operations research specialists will find this book stimulating, challenging, and an asset to their work. 1993 Statistics for Spatial Data, Revised Edition Noel Cressie, Iowa State University, USA Designed for the scientific and engineering professional eager to exploit its enormous potential, Statistics for Spatial Data is a primer to the theory as well as the nuts-and-bolts of this influential technique. Focusing on the three areas of geostatistical data, lattice data, and point patterns, the book sheds light on the link between data and model, and reveals how spatial statistical models can be used to solve a host of problems in science and engineering. The previous edition was hailed by Mathematical Reviews as "an excellent book which…will become a basic reference". Revised to reflect state-of-the-art developments, this edition also features many detailed examples, numerous illustrations, and over 1000 references. The first fully comprehensive introduction, Statistics for Spatial Data is an essential guide for professionals in biology, earth sciences, civil, electrical and agricultural engineering, geography, epidemiology, and ecology. 1993

Now in its second edition, this textbook provides an introduction to Python and its use for statistical data analysis. It covers common statistical tests for continuous, discrete and categorical data, as well as linear regression analysis and topics from survival analysis and Bayesian statistics. For this new edition, the introductory chapters on Python, data input and visualization have been reworked and updated. The chapter on experimental design has been expanded, and programs for the determination of confidence intervals commonly used in quality control have been introduced. The book also features a new chapter on finding patterns in data, including time series. A new appendix describes useful programming tools, such as testing tools, code repositories, and GUIs. The provided working code for Python solutions, together with easy-to-follow examples, will reinforce the reader's immediate understanding of the topic. Accompanying data sets and Python programs are also available online. With recent advances in the Python ecosystem, Python has become a popular language for scientific computing, offering a powerful environment for statistical data analysis. With examples drawn mainly from the life and medical sciences, this book is intended primarily for masters and PhD students. As it provides the required statistics background, the book can also be used by anyone who wants to perform a statistical data analysis.

Features content that has been used extensively in a university setting, allowing the reader to benefit from tried and tested methods, practices, and knowledge. In contrast to existing books on the market, it details the specialized packages that have been developed over the past decade, and focuses on pulling real-time data directly from free data sources on the internet. It achieves its goal by providing a large number of examples in hot topics such as machine learning. Assumes no prior knowledge of R, allowing it to be useful to a range of people from undergraduates to professionals. Comprehensive explanations make the reader proficient in a multitude of advanced methods, and provides overviews of many different resources that will be useful to the readers.

Providing an easy explanation of the fundamentals, methods, and applications of chemometrics

- Acts as a practical guide to multivariate data analysis techniques- Explains the methods used in Chemometrics and teaches the reader to perform all relevant calculations- Presents the basic chemometric methods as worksheet functions in Excel- Includes Chemometrics Add In for download which uses Microsoft Excel(R) for chemometrics training- Online downloads includes workbooks with examples

'Fascinating . . . timely' Daily Mail 'Refreshingly clear and engaging' Tim Harford 'Delightful . . . full of unique insights' Prof Sir David Spiegelhalter There's no getting away from statistics. We encounter them every day. We are all users of statistics whether we like it or not. Do missed appointments really cost the NHS GBP1bn per year? What's the difference between the mean gender pay gap and the median gender pay gap? How can we work out if a claim that we use 42 billion single-use plastic straws per year in the UK is accurate? What did the Vote Leave campaign's GBP350m bus really mean? How can we tell if the headline 'Public pensions cost you GBP4,000 a year' is correct? Does snow really cost the UK economy GBP1bn per day? But how do we distinguish statistical fact from fiction? What can we do to decide whether a number, claim or news story is accurate? Without an understanding of data, we cannot truly understand what is going on in the world around us. Written by Anthony Reuben, the BBC's first head of statistics, Statistical is an accessible and empowering guide to challenging the numbers all around us.

This book focuses on tools and techniques for building regression models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to base inferences or conclusions only on valid models. Plots are shown to be an important tool for both building regression models and assessing their validity. We shall see that deciding what to plot and how each plot should be interpreted will be a major challenge. In order to overcome this challenge we shall need to understand the mathematical properties of the fitted regression models and associated diagnostic procedures. As such this will be an area of focus throughout the book. In particular, we shall carefully study the properties of resi- als in order to understand when patterns in residual plots provide direct information about model misspecification and when they do not. The regression output and plots that appear throughout the book have been gen- ated using R. The output from R that appears in this book has been edited in minor ways. On the book web site you will find the R code used in each example in the text.

This volume, which is completely dedicated to continuous bivariate dist- butions, describes in detail their forms, properties, dependence structures, computation, and applications. It is a comprehensive and thorough revision ofanearliereditionof"ContinuousBivariateDistributions, Emphasizing- plications" by T.P. Hutchinson and C.D. Lai, published in 1990 by Rumsby Scienti?c Publishing, Adelaide, Australia. It has been nearly two decades since the publication of that book, and much has changed in this area of research during this period. Generali- tions have been considered for many known standard bivariate distributions. Skewed versions of di?erent bivariate distributions have been proposed and appliedtomodeldatawithskewnessdepartures.Byspecifyingthetwocon- tional distributions, rather than the simple speci?cation of one marginal and one conditional distribution, several general families of conditionally spe- ?ed bivariate distributions have been derived and studied at great length. Finally, bivariate distributions generated by a variety of copulas and their ?exibility (in terms of accommodating association/correlation) and str- tural properties have received considerable attention. All these developments andadvancesnecessitatedthepresentvolumeandhavethusresultedinas- stantially di?erent version than the last edition, both in terms of coverage and topics of discussion.

This book presents a general method for deriving higher-order statistics of multivariate distributions with simple algorithms that allow for actual calculations. Multivariate nonlinear statistical models require the study of higher-order moments and cumulants. The main tool used for the definitions is the tensor derivative, leading to several useful expressions concerning Hermite polynomials, moments, cumulants, skewness, and kurtosis. A general test of multivariate skewness and kurtosis is obtained from this treatment. Exercises are provided for each chapter to help the readers understand the methods. Lastly, the book includes a comprehensive list of references, equipping readers to explore further on their own.