Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This text explores a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric. It is the first book on this topic. The text is intended for first-year graduate students in statistics and learning theory, and offers a host of opportunities for further research and thesis topics. Each chapter corresponds roughly to one lecture, and is supplemented with many classroom exercises. A one year course in probability theory at the level of Feller's Volume 1 should be more than adequate preparation. Gabor Lugosi is Professor at Universitat Pompeu Fabra in Barcelona, and Luc Debroye is Professor at McGill University in Montreal. In 1996, the authors, together with Lászlo Györfi, published the successful text, A Probabilistic Theory of Pattern Recognition with Springer-Verlag. Both authors have made many contributions in the area of nonparametric estimation.

This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability. The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.

This book establishes a unified framework for dealing with typical engineering complications arising in modern, complex, large-scale networks such as parameter uncertainties, missing measurement and cyber-attack. Distributed Filtering, Control and Synchronization is a timely reflection on methods designed to handle a series of control and signal-processing issues in modern industrial engineering practice in areas like power grids and environmental monitoring. It exploits the latest techniques to handle the emerging mathematical and computational challenges arising from, among other things, the dynamic topologies of distributed systems and in the context of sensor networks and multi-agent systems. These techniques include recursive linear matrix inequalities, local-performance and stochastic analyses and techniques based on matrix theory. Readers interested in the theory and application of control and signal processing will find much to interest them in the new models and methods presented in this book. Academic researchers can find ideas for developing their own research, graduate and advanced undergraduate students will be made aware of the state of the art, and practicing engineers will find methods for addressing practical difficulties besetting modern networked systems

This book addresses many of the gaps in how industry and academia are currently tackling problems associated with big data. It introduces novel concepts, describes the end-to-end process, and connects the various pieces of the puzzle to offer a holistic view. In addition, it explains important concepts for a wide audience, using accessible language, diagrams, examples and analogies to do so. The book is intended for readers working in industry who want to expand their knowledge or pursue a related degree, and employs an industry-centered perspective.

This book introduces the advances in synchromodal logistics and provides a framework to classify various optimisation problems in this field. It explores the application of this framework to solve a broad range of problems, such as problems with and without a central decision-maker, problems with and without full information, deterministic problems, problems coping with uncertainty, optimisation of a full network design problem. It covers theoretical constructs, such as discrete optimisation, robust optimisation, optimisation under uncertainty, multi-objective optimisation and agent based equilibrium models. Moreover, practical elaborated use cases are presented to deepen understanding. The book gives both researchers and practitioners a good overview of the field of synchromodal optimisation problems and offers the reader practical methods for modelling and problem-solving.

This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations. It is intended for beginning graduate students in mathematics or researchers in physics or engineering. As with the introductory book entitled "Harmonic Analysis on Symmetric Spaces - Euclidean Space, the Sphere, and the Poincare Upper Half Plane, the style is informal with an emphasis on motivation, concrete examples, history, and applications. The symmetric spaces considered here are quotients X=G/K, where G is a non-compact real Lie group, such as the general linear group GL(n,P) of all n x n non-singular real matrices, and K=O(n), the maximal compact subgroup of orthogonal matrices. Other examples are Siegel's upper half "plane" and the quaternionic upper half "plane". In the case of the general linear group, one can identify X with the space Pn of n x n positive definite symmetric matrices. Many corrections and updates have been incorporated in this new edition. Updates include discussions of random matrix theory and quantum chaos, as well as recent research on modular forms and their corresponding L-functions in higher rank. Many applications have been added, such as the solution of the heat equation on Pn, the central limit theorem of Donald St. P. Richards for Pn, results on densest lattice packing of spheres in Euclidean space, and GL(n)-analogs of the Weyl law for eigenvalues of the Laplacian in plane domains. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, fundamental domains in X for discrete groups (such as the modular group GL(n,Z) of n x n matrices with integer entries and determinant +/-1), connections with the problem of finding densest lattice packings of spheres in Euclidean space, automorphic forms, Hecke operators, L-functions, and the Selberg trace formula and its applications in spectral theory as well as number theory.

This handbook will provide both overviews of statistical methods in sports and in-depth treatment of critical problems and challenges confronting statistical research in sports. The material in the handbook will be organized by major sport (baseball, football, hockey, basketball, and soccer) followed by a section on other sports and general statistical design and analysis issues that are common to all sports. This handbook has the potential to become the standard reference for obtaining the necessary background to conduct serious statistical analyses for sports applications and to appreciate scholarly work in this expanding area.

This book presents the latest findings on statistical inference in multivariate, multilinear and mixed linear models, providing a holistic presentation of the subject. It contains pioneering and carefully selected review contributions by experts in the field and guides the reader through topics related to estimation and testing of multivariate and mixed linear model parameters. Starting with the theory of multivariate distributions, covering identification and testing of covariance structures and means under various multivariate models, it goes on to discuss estimation in mixed linear models and their transformations. The results presented originate from the work of the research group Multivariate and Mixed Linear Models and their meetings held at the Mathematical Research and Conference Center in Bedlewo, Poland, over the last 10 years. Featuring an extensive bibliography of related publications, the book is intended for PhD students and researchers in modern statistical science who are interested in multivariate and mixed linear models.

This book constitutes a selection of the best papers from the 15th International Conference on Business Excellence, Digital Economy and New Value Creation, ICBE 2021, held in Bucharest, Romania, in March 2021. This book is a collection of research findings and perspectives related to the digital economy and new value creation, led by the set of improvements and changes in the economic, societal and technological structures and processes towards the effort of reaching the sustainability goals.

Iterative Methods for Queuing and Manufacturing Systems introduces the recent advances and developments in iterative methods for solving Markovian queuing and manufacturing problems.Key highlights include:- an introduction to simulation and simulation software packages;- Markovian models with applications in inventory control and supply chains; future research directions.With numerous exercises and fully-worked examples, this book will be essential reading for anyone interested in the formulation and computation of queuing and manufacturing systems but it will be of particular interest to students, practitioners and researchers in Applied Mathematics, Scientific Computing and Operational Research.

Content-Based Analysis Of Digital Video focuses on fundamental issues underlying the development of content access mechanisms for digital video. It treats topics that are critical to successfully automating the video content extraction and retrieval processes, and includes coverage of:

- Video parsing,

- Video content indexing and representation,

- Affective video content analysis. In this well illustrated book the author integrates related information currently scattered throughout the literature and combines it with new ideas into a unified theoretical approach to video content analysis. The material also suggests ideas for future research.
Systems developers, researchers and students working in the area of content-based analysis and retrieval of video and multimedia in general will find this book invaluable.

This book provides retail managers with a practical guide to using data. It covers three topics that are key areas of innovation for retailers: Algorithmic Marketing, Logistics, and Pricing. Use cases from these areas are presented and discussed in a conceptual and comprehensive manner. Retail managers will learn how data analysis can be used to optimize pricing, customer loyalty and logistics without complex algorithms. The goal of the book is to help managers ask the right questions during a project, which will put them on the path to making the right decisions. It is thus aimed at practitioners who want to use advanced techniques to optimize their retail organization.

The objective of the book is to acquaint the reader with the use of queueing theory in the analysis of manufacturing systems.

A look at baseball data from a statistical modeling perspective! There is a fascination among baseball fans and the media to collect data on every imaginable event during a baseball game and this book addresses a number of questions that are of interest to many baseball fans. These include how to rate players, predict the outcome of a game or the attainment of an achievement, making sense of situational data, and deciding the most valuable players in the World Series. Aimed at a general audience, the text does not assume any prior background in probability or statistics, although a knowledge of high school abgebra will be helpful.

This second edition of G. Winkler's successful book on random field approaches to image analysis, related Markov Chain Monte Carlo methods, and statistical inference with emphasis on Bayesian image analysis concentrates more on general principles and models and less on details of concrete applications. Addressed to students and scientists from mathematics, statistics, physics, engineering, and computer science, it will serve as an introduction to the mathematical aspects rather than a survey. Basically no prior knowledge of mathematics or statistics is required.The second edition is in many parts completely rewritten and improved, and most figures are new. The topics of exact sampling and global optimization of likelihood functions have been added. This second edition comes with a CD-ROM by F. Friedrich,containing a host of (live) illustrations for each chapter. In an interactive environment, readers can perform their own experiments to consolidate the subject.

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.

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.

The principal focus here is on autoregressive moving average models and analogous random fields, with probabilistic and statistical questions also being discussed. The book contrasts Gaussian models with noncausal or noninvertible (nonminimum phase) non-Gaussian models and deals with problems of prediction and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted. Intended as a text for gradutes in statistics, mathematics, engineering, the natural sciences and economics, the only recommendation is an initial background in probability theory and statistics. Notes on background, history and open problems are given at the end of the book.

In this thesis, the first measurement of the running of the top quark mass is presented. This is a fundamental quantum effect that had never been studied before. Any deviation from the expected behaviour can be interpreted as a hint of the presence of physics beyond the Standard Model. All relevant aspects of the analysis are extensively described and documented. This thesis also describes a simultaneous measurement of the inclusive top quark-antiquark production cross section and the top quark mass in the simulation. The measured cross section is also used to precisely determine the values of the top quark mass and the strong coupling constant by comparing to state-of-the-art theoretical predictions. All the theoretical and experimental aspects relevant to the results presented in this thesis are discussed in the initial chapters in a concise but complete way, which makes the material accessible to a wider audience.

This book is the third edition of a successful textbook for upper-undergraduate and early graduate students, which offers a solid foundation in probability theory and statistics and their application to physical sciences, engineering, biomedical sciences and related disciplines. It provides broad coverage ranging from conventional textbook content of probability theory, random variables, and their statistics, regression, and parameter estimation, to modern methods including Monte-Carlo Markov chains, resampling methods and low-count statistics. In addition to minor corrections and adjusting structure of the content, particular features in this new edition include: Python codes and machine-readable data for all examples, classic experiments, and exercises, which are now more accessible to students and instructors New chapters on low-count statistics including the Poisson-based Cash statistic for regression in the low-count regime, and on contingency tables and diagnostic testing. An additional example of classic experiments based on testing data for SARS-COV-2 to demonstrate practical applications of the described statistical methods. This edition inherits the main pedagogical method of earlier versions-a theory-then-application approach-where emphasis is placed first on a sound understanding of the underlying theory of a topic, which becomes the basis for an efficient and practical application of the materials. Basic calculus is used in some of the derivations, and no previous background in probability and statistics is required. The book includes many numerical tables of data as well as exercises and examples to aid the readers' understanding of the topic.

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.

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.

A self-contained and coherent account of probabilistic techniques, covering: distance measures, kernel rules, nearest neighbour rules, Vapnik-Chervonenkis theory, parametric classification, and feature extraction. Each chapter concludes with problems and exercises to further the readers understanding. Both research workers and graduate students will benefit from this wide-ranging and up-to-date account of a fast- moving field.

Queues for service of one kind or another arise in many different fields of activity. In recent years a considerable amount of research has been conducted into the properties of simplified mathematical models of such queueing systems. Our objects in the present mono graph are threefold. First we have tried, especially in Chapter I, to give an account of the general ideas that are useful in describing and thinking about queueing systems. Secondly, we have illustrated by examples some of the mathematical techniques that are useful for the study of these systems. Finally, we have given some explicit mathematical results which may be useful in practical investigations. A recent bibliography gave some 600 papers on queueing and allied subjects. Clearly we cannot, in the modest limits of the present work, cover more than a small proportion of the huge amount of material available. However, some results that we have not had space to discuss in detail have been given in outline in the form of exercises."