Masatoshi Fukushima is one of the most influential probabilists of our times. His fundamental work on Dirichlet forms and Markov processes made Hilbert space methods a tool in stochastic analysis and by this he opened the way to several new developments. His impact on a new generation of probabilists can hardly be overstated. These Selecta collect 25 of Fukushima's seminal articles published between 1967 and 2007.

This is the second edition of a coherent introduction to the subject of asymptotic statistics as it has developed over the past 50 years. It differs from the first edition in that it is now more 'reader friendly' and also includes a new chapter on Gaussian and Poisson experiments, reflecting their growing role in the field. Most of the subsequent chapters have been entirely rewritten and the nonparametrics of Chapter 7 have been amplified. The volume is not intended to replace monographs on specialized subjects, but will help to place them in a coherent perspective. It thus represents a link between traditional material - such as maximum likelihood, and Wald's Theory of Statistical Decision Functions -- together with comparison and distances for experiments. Much of the material has been taught in a second year graduate course at Berkeley for 30 years.

The fascinating correspondence between Paul Levy and Maurice Frechet spans an extremely active period in French mathematics during the twentieth century. The letters of these two Frenchmen show their vicissitudes of research and passionate enthusiasm for the emerging field of modern probability theory. The letters cover various topics of mathematical importance including academic careers and professional travels, issues concerning students and committees, and the difficulties both mathematicians met to be elected to the Paris Academy of Sciences. The technical questions that occupied Levy and Frechet on almost a daily basis are the primary focus of these letters, which are charged with elation, frustration and humour. Their mathematical victories and setbacks unfolded against the dramatic backdrop of the two World Wars and the occupation of France, during which Levy was obliged to go into hiding. The clear and persistent desire of these mathematicians to continue their work whatever the circumstance testifies to the enlightened spirit of their discipline which was persistent against all odds. The book contains a detailed and comprehensive introduction to the central topics of the correspondence. The original text of the letters is also annotated by numerous footnotes for helpful guidance. Paul Levy and Maurice Frechet will be useful to anybody interested in the history of mathematics in the twentieth century and, in particular, the birth of modern probab ility theory.

The present monograph on stochastic Komatu-Loewner evolutions (SKLEs) provides the first systematic extension of the Schramm-Loewner evolution (SLE) theory from a simply connected planar domain to multiply connected domains by using the Brownian motion with darning (BMD) that has arisen in a recent study of the boundary theory of symmetric Markov processes.This volume is presented in an accessible manner for the interested researchers and graduate students. It also brings new insights into SLEs as special cases of SKLEs. Mathematically, it can be viewed as a powerful application of stochastic analysis via BMDs to complex analysis.

Requires minimal prerequisites Explained in basic terms Illustrated with binary datasets and real life examples Covers primary concepts and methods Accessible to undergraduates Suitable for a heterogeneous audience

This book brings together the latest findings in the area of stochastic analysis and statistics. The individual chapters cover a wide range of topics from limit theorems, Markov processes, nonparametric methods, acturial science, population dynamics, and many others. The volume is dedicated to Valentin Konakov, head of the International Laboratory of Stochastic Analysis and its Applications on the occasion of his 70th birthday. Contributions were prepared by the participants of the international conference of the international conference "Modern problems of stochastic analysis and statistics", held at the Higher School of Economics in Moscow from May 29 - June 2, 2016. It offers a valuable reference resource for researchers and graduate students interested in modern stochastics.

Space is increasingly recognized as a legitimate factor that influences many processes and conceptual frameworks, including notions of spatial coherence and spatial heterogeneity that have been demonstrated to provide substance to both theory and explanation. The potential and relevance of spatial analysis is increasingly understood by an expanding sphere of cogent disciplines that have adopted the tools of spatial analysis. This book brings together major new developments in spatial analysis techniques, including spatial statistics, econometrics, and spatial visualization, and applications to fields such as regional studies, transportation and land use, political and economic geography, population and health. Establishing connections to existing and emerging lines of research, the book also serves as a survey of the field of spatial analysis and its links with related areas.

This monograph is multivariate, multi-perspective and multipurpose. We intend to be innovatively integrative through statistical synthesis. Innovation requires capacity to operate in ways that are not ordinary, which means that conventional computations and generic graphics will not meet the needs of an adaptive approach. Flexible formulation and special schematics are essential elements that must be manageable and economical."

This book is compilation of different analytics and machine learning techniques focusing on the tourism industry, particularly in measuring the impact of COVID-19 as well as forging a path ahead toward recovery. It includes case studies on COVID-19's effects on tourism in Europe, Hong Kong, China, and Singapore with the objective of looking at the issues through a data analytical lens and uncovering potential solutions. It adopts descriptive analytics, predictive analytics, machine learning predictive models, and some simulation models to provide holistic understanding. There are three ways in which readers will benefit from reading this work. Firstly, readers gain an insightful understanding of how tourism is impacted by different factors, its intermingled relationship with macro and business data, and how different analytics approaches can be used to visualize the issues, scenarios, and resolutions. Secondly, readers learn to pick up data analytics skills from the illustrated examples. Thirdly, readers learn the basics of Python programming to work with the different kinds of datasets that may be applicable to the tourism industry.

Designed to help you overcome your apprehension about statistics, UNDERSTANDING BASIC STATISTICS, ENHANCED, 7E, INTERNATIONAL METRIC EDITION provides plenty of guidance and informal advice as it demonstrates the links between statistics and the real world. The text's reader-friendly approach helps you grasp the concepts and see how they relate to your life. A complete technology package, including JMP (R) statistical software, gives you the tools you need to practice what you're learning and succeed in the course.

Conventional statistical methods have a very serious flaw. They routinely miss differences among groups or associations among variables that are detected by more modern techniques, even under very small departures from normality. Hundreds of journal articles have described the reasons standard techniques can be unsatisfactory, but simple, intuitive explanations are generally unavailable. Situations arise where even highly nonsignificant results become significant when analyzed with more modern methods.

Without assuming the reader has any prior training in statistics, Part I of this book describes basic statistical principles from a point of view that makes their shortcomings intuitive and easy to understand. The emphasis is on verbal and graphical descriptions of concepts. Part II describes modern methods that address the problems covered in Part I. Using data from actual studies, many examples are included to illustrate the practical problems with conventional procedures and how more modern methods can make a substantial difference in the conclusions reached in many areas of statistical research.

The second edition of this book includes a number of advances and insights that have occurred since the first edition appeared. Included are new results relevant to medians, regression, measures of association, strategies for comparing dependent groups, methods for dealing with heteroscedasticity, and measures of effect size.

This book brings together aspects of statistics and machine learning to provide a comprehensive guide to evaluating, interpreting and understanding biometric data. It naturally leads to topics including data mining and prediction to be examined in detail. The book places an emphasis on the various performance measures available for biometric systems, what they mean, and when they should and should not be applied. The evaluation techniques are presented rigorously, however they are always accompanied by intuitive explanations. This is important for the increased acceptance of biometrics among non-technical decision makers, and ultimately the general public.

This book summarizes developments related to a class of methods called Stochastic Decomposition (SD) algorithms, which represent an important shift in the design of optimization algorithms. Unlike traditional deterministic algorithms, SD combines sampling approaches from the statistical literature with traditional mathematical programming constructs (e.g. decomposition, cutting planes etc.). This marriage of two highly computationally oriented disciplines leads to a line of work that is most definitely driven by computational considerations. Furthermore, the use of sampled data in SD makes it extremely flexible in its ability to accommodate various representations of uncertainty, including situations in which outcomes/scenarios can only be generated by an algorithm/simulation. The authors report computational results with some of the largest stochastic programs arising in applications. These results (mathematical as well as computational) are the tip of the iceberg'. Further research will uncover extensions of SD to a wider class of problems. Audience: Researchers in mathematical optimization, including those working in telecommunications, electric power generation, transportation planning, airlines and production systems. Also suitable as a text for an advanced course in stochastic optimization.

Entropy optimization is a useful combination of classical engineering theory (entropy) with mathematical optimization. The resulting entropy optimization models have proved their usefulness with successful applications in areas such as image reconstruction, pattern recognition, statistical inference, queuing theory, spectral analysis, statistical mechanics, transportation planning, urban and regional planning, input-output analysis, portfolio investment, information analysis, and linear and nonlinear programming. While entropy optimization has been used in different fields, a good number of applicable solution methods have been loosely constructed without sufficient mathematical treatment. A systematic presentation with proper mathematical treatment of this material is needed by practitioners and researchers alike in all application areas. The purpose of this book is to meet this need. Entropy Optimization and Mathematical Programming offers perspectives that meet the needs of diverse user communities so that the users can apply entropy optimization techniques with complete comfort and ease. With this consideration, the authors focus on the entropy optimization problems in finite dimensional Euclidean space such that only some basic familiarity with optimization is required of the reader.

The three decades which have followed the publication of Heinz Neudecker's seminal paper `Some Theorems on Matrix Differentiation with Special Reference to Kronecker Products' in the Journal of the American Statistical Association (1969) have witnessed the growing influence of matrix analysis in many scientific disciplines. Amongst these are the disciplines to which Neudecker has contributed directly - namely econometrics, economics, psychometrics and multivariate analysis. This book aims to illustrate how powerful the tools of matrix analysis have become as weapons in the statistician's armoury. The majority of its chapters are concerned primarily with theoretical innovations, but all of them have applications in view, and some of them contain extensive illustrations of the applied techniques. This book will provide research workers and graduate students with a cross-section of innovative work in the fields of matrix methods and multivariate statistical analysis. It should be of interest to students and practitioners in a wide range of subjects which rely upon modern methods of statistical analysis. The contributors to the book are themselves practitioners of a wide range of subjects including econometrics, psychometrics, educational statistics, computation methods and electrical engineering, but they find a common ground in the methods which are represented in the book. It is envisaged that the book will serve as an important work of reference and as a source of inspiration for some years to come.

This book addresses the problem of multi-agent systems, considering that it can be interpreted as a generalized multi-synchronization problem. From manufacturing tasks, through encryption and communication algorithms, to high-precision experiments, the simultaneous cooperation between multiple systems or agents is essential to successfully carrying out different modern activities, both in academy and industry. For example, the coordination of multiple assembler robots in manufacturing lines. These agents need to synchronize. The first two chapters of the book describe the synchronization of dynamical systems, paying special attention to the synchronization of non-identical systems. Following, the third chapter presents an interesting application of the synchronization phenomenon for state estimation. Subsequently, the authors fully address the multi-agent problem interpreted as multi-synchronization. The final chapters introduce the reader to a more complex problem, the synchronization of systems governed by partial differential equations, both of integer and fractional order. The book aimed at graduates, postgraduate students and researchers closely related to the area of automatic control. Previous knowledge of linear algebra, classical and fractional calculus is requested, as well as some fundamental notions of graph theory.

The subject of multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This introductory text provides students and researchers in the above fields with various ways of handling some of the useful but difficult concepts encountered in dealing with the machinery of multivariable analysis and differential forms on manifolds. The approach here is to make such concepts as concrete as possible.

Highlights and key features:

* systematic exposition, supported by numerous examples and exercises from the computational to the theoretical

* brief development of linear algebra in Rn

* review of the elements of metric space theory

* treatment of standard multivariable material: differentials as linear transformations, the inverse and implicit function theorems, Taylor's theorem, the change of variables for multiple integrals (the most complex proof in the book)

* Lebesgue integration introduced in concrete way rather than via measure theory

* latar chapters move beyond Rn to manifolds and analysis on manifolds, covering the wedge product, differential forms, and the generalized Stokes' theorem

* bibliography and comprehensive index

Core topics in multivariable analysis that are basic for senior undergraduates and graduate studies in differential geometry and for analysis in N dimensions and on manifolds are covered. Aside from mathematical maturity, prerequisites are a one-semester undergraduate course in advanced calculus or analysis, and linear algebra. Additionally, researchers working in the areas of dynamical systems, control theory and optimization, general relativity and electromagnetic phenomena may use the book as a self-study resource.

Parametric and semiparametric models are tools with a wide range of applications to reliability, survival analysis, and quality of life. This self-contained volume examines these tools in survey articles written by experts currently working on the development and evaluation of models and methods. While a number of chapters deal with general theory, several explore more specific connections and recent results in "real-world" reliability theory, survival analysis and related fields.

Specific topics covered include:

* non-parametric estimation of lifetimes of subjects exposed to radiation

* statistical analysis of simultaneous degradation-mortality data with covariates of the aged

* estimation of maintenance efficiency in semiparametric imperfect repair models

* cancer prognosis using survival forests

* short-term health problems related to air pollution: analysis using semiparametric generalized additive models

* parametric models in accelerated life testing and fuzzy data

* semiparametric models in the studies of aging and longevity

This book will be of use as a reference text for general statisticians, theoreticians, graduate students, reliability engineers, health researchers, and biostatisticians working in applied probability and statistics.

Statistical Design, Monitoring, and Analysis of Clinical Trials, Second Edition concentrates on the biostatistics component of clinical trials. This new edition is updated throughout and includes five new chapters. Developed from the authors' courses taught to public health and medical students, residents, and fellows during the past 20 years, the text shows how biostatistics in clinical trials is an integration of many fundamental scientific principles and statistical methods. The book begins with ethical and safety principles, core trial design concepts, the principles and methods of sample size and power calculation, and analysis of covariance and stratified analysis. It then focuses on sequential designs and methods for two-stage Phase II cancer trials to Phase III group sequential trials, covering monitoring safety, futility, and efficacy. The authors also discuss the development of sample size reestimation and adaptive group sequential procedures, phase 2/3 seamless design and trials with predictive biomarkers, exploit multiple testing procedures, and explain the concept of estimand, intercurrent events, and different missing data processes, and describe how to analyze incomplete data by proper multiple imputations. This text reflects the academic research, commercial development, and public health aspects of clinical trials. It gives students and practitioners a multidisciplinary understanding of the concepts and techniques involved in designing, monitoring, and analyzing various types of trials. The book's balanced set of homework assignments and in-class exercises are appropriate for students and researchers in (bio)statistics, epidemiology, medicine, pharmacy, and public health.

This book covers research work spanning the breadth of ventures, a variety of challenges and the finest of techniques used to address data and analytics, by subject matter experts from the business world. The content of this book highlights the real-life business problems that are relevant to any industry and technology environment. This book helps us become a contributor to and accelerator of artificial intelligence, data science and analytics, deploy a structured life-cycle approach to data related issues, apply appropriate analytical tools & techniques to analyze data and deliver solutions with a difference. It also brings out the story-telling element in a compelling fashion using data and analytics. This prepares the readers to drive quantitative and qualitative outcomes and apply this mindset to various business actions in different domains such as energy, manufacturing, health care, BFSI, security, etc.

Stochastic elasticity is a fast developing field that combines nonlinear elasticity and stochastic theories in order to significantly improve model predictions by accounting for uncertainties in the mechanical responses of materials. However, in contrast to the tremendous development of computational methods for large-scale problems, which have been proposed and implemented extensively in recent years, at the fundamental level, there is very little understanding of the uncertainties in the behaviour of elastic materials under large strains. Based on the idea that every large-scale problem starts as a small-scale data problem, this book combines fundamental aspects of finite (large-strain) elasticity and probability theories, which are prerequisites for the quantification of uncertainties in the elastic responses of soft materials. The problems treated in this book are drawn from the analytical continuum mechanics literature and incorporate random variables as basic concepts along with mechanical stresses and strains. Such problems are interesting in their own right but they are also meant to inspire further thinking about how stochastic extensions can be formulated before they can be applied to more complex physical systems.

Enrique Castillo is a leading figure in several mathematical and engineering fields. Organized to honor Castillo 's significant contributions, this volume is an outgrowth of the "International Conference on Mathematical and Statistical Modeling," and covers recent advances in the field. Applications to safety, reliability and life-testing, financial modeling, quality control, general inference, as well as neural networks and computational techniques are presented.

This volume dedicated to William Q. Meeker on the occasion of his sixtieth birthday is a collection of invited chapters covering recent advances in accelerated life testing and degradation models. The book covers a wide range of applications to areas such as reliability, quality control, the health sciences, economics and finance. Additional topics covered include accelerated testing and inference, step-stress testing and inference, nonparametric inference, model validity in accelerated testing, the point process approach, bootstrap methods in degradation analysis, exact inferential methods in reliability, dynamic perturbed systems, and degradation models in statistics. Advances in Degradation Modeling is an excellent reference for researchers and practitioners in applied probability and statistics, industrial statistics, the health sciences, quality control, economics, and finance.

This book is an extension of the author's first book and serves as a guide and manual on how to specify and compute 2-, 3-, and 4-Event Bayesian Belief Networks (BBN). It walks the learner through the steps of fitting and solving fifty BBN numerically, using mathematical proof. The author wrote this book primarily for inexperienced learners as well as professionals, while maintaining a proof-based academic rigor. The author's first book on this topic, a primer introducing learners to the basic complexities and nuances associated with learning Bayes' theorem and inverse probability for the first time, was meant for non-statisticians unfamiliar with the theorem-as is this book. This new book expands upon that approach and is meant to be a prescriptive guide for building BBN and executive decision-making for students and professionals; intended so that decision-makers can invest their time and start using this inductive reasoning principle in their decision-making processes. It highlights the utility of an algorithm that served as the basis for the first book, and includes fifty 2-, 3-, and 4-event BBN of numerous variants.