The dynamics of population systems cannot be understood within the framework of ordinary differential equations, which assume that the number of interacting agents is infinite. With recent advances in ecology, biochemistry and genetics it is becoming increasingly clear that real systems are in fact subject to a great deal of noise. Relevant examples include social insects competing for resources, molecules undergoing chemical reactions in a cell and a pool of genomes subject to evolution.When the population size is small, novel macroscopic phenomena can arise, which can be analyzed using the theory of stochastic processes. This thesis is centered on two unsolved problems in population dynamics: the symmetry breaking observed in foraging populations and the robustness of spatial patterns. We argue that these problems can be resolved with the help of two novel concepts: noise-induced bistable states and stochastic patterns.
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A useful introduction to this topic for both students and researchers, with an emphasis on applications and practicalities rather than on a formal development. It is based on the popular software package for graphical modelling, MIM, freely available for downloading from the Internet. Following a description of some of the basic ideas of graphical modelling, subsequent chapters describe particular families of models, including log-linear models, Gaussian models, and models for mixed discrete and continuous variables. Further chapters cover hypothesis testing and model selection. Chapters 7 and 8 are new to this second edition and describe the use of directed, chain, and other graphs, complete with a summary of recent work on causal inference.

Intended for graduates and researchers in physics, chemistry, biology, and applied mathematics, this book provides an up-to-date introduction to current research in fluctuations in spatially extended systems. It covers the theory of stochastic partial differential equations and gives an overview of the effects of external noise on dynamical systems with spatial degrees of freedom. Starting with a general introduction to noise-induced phenomena in dynamical systems, the text moves on to an extensive discussion of analytical and numerical tools needed to gain information from stochastic partial differential equations. It then turns to particular problems described by stochastic PDEs, covering a wide part of the rich phenomenology of spatially extended systems, such as nonequilibrium phase transitions, domain growth, pattern formation, and front propagation. The only prerequisite is a minimal background knowledge of the Langevin and Fokker-Planck equations.

Statistics for Engineers and Scientists stands out for its clear presentation of applied statistics. The book takes a practical approach to methods of statistical modeling and data analysis that are most often used in scientific work. This edition features a unique approach highlighted by an engaging writing style that explains difficult concepts clearly, along with the use of contemporary real world data sets, to help motivate students and show direct connections to industry and research. While focusing on practical applications of statistics, the text makes extensive use of examples to motivate fundamental concepts and to develop intuition. The new edition of Statistics for Engineers and Scientists is also available in McGraw Hill Connect, featuring SmartBook 2.0, Adaptive Learning Assignments, and more!

This volume in the Synthese Library Series is the result of a con- ference held at the Roskilde University, Denmark, September 16- 18, 1998. The purpose of this meeting was to shed light on some of the recent issues in probability theory and track their history; to analyze their philosophical and mathematical significance, and to analyze the role of mathematical probability theory in other sciences. Hence the conference was called Probability Theory- Philosophy! Recent History and Relations to Science. The editors would like to thank the invited speakers includ- ing in alphabetical order Prof. N.H. Bingham (BruneI Univer- sity), Prof. Berna KIlmc; (Bogazici University), Prof. Eberhard Knoblock (Techniche Universitat Berlin), Prof. J.B. Paris (Uni- versity of Manchester), Prof. T. Seidenfeld (Carnegie Mellon University), Prof. Glenn Shafer (Rutgers University) and Prof. Volodya Vovk (University of London) for contributing, in the most lucid and encouraging way, to the fulfillment of the con- ference aim. The editors are also grateful to the invited speakers for making their contributions available for publication. The conference was organized by the Danish Network on the History and Philosophy of Mathematics http://mmf.ruc.dkjmathnetj The editors would like to thank the network's organizing com- mittee consisting of Prof. Kirsti Andersen (University of Aarhus), Prof. Jesper Liitzen (University of Copenhagen), Dr. Tinne Hoff Kjeldsen (Roskilde University) and the committee's secretaries Lise Mariane Jeppesen and Jesper Thrane (Roskilde University).

This book presents contributions and review articles on the theory of copulas and their applications. The authoritative and refereed contributions review the latest findings in the area with emphasis on "classical" topics like distributions with fixed marginals, measures of association, construction of copulas with given additional information, etc. The book celebrates the 75th birthday of Professor Roger B. Nelsen and his outstanding contribution to the development of copula theory. Most of the book's contributions were presented at the conference "Copulas and Their Applications" held in his honor in Almeria, Spain, July 3-5, 2017. The chapter 'When Gumbel met Galambos' is published open access under a CC BY 4.0 license.

This is the first book where mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep mathematical approaches. It contains a collection of refereed papers presented at the Colloquium on Mathematics and Computer Science held at the University of Versailles-St-Quentin on September 18-20, 2000. The colloquium was a meeting place for researchers in mathematics and computer science and thus an important opportunity to exchange ideas and points of view, and to present new approaches and new results in the common areas such as algorithms analysis, trees, combinatorics, optimization, performance evaluation and probabilities. The book is intended for a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. It provides an overview of the current questions in computer science and related modern mathematical methods. The range of applications is very wide and reaches beyond computer science.

This volume presents the results of biological and medical research with the statistical methods used to obtain them. Nowadays the fields of biology and experimental medicine rely on techniques for processing of experimental data and for the evaluation of hypotheses. It is increasingly necessary to stimulate awareness of the importance of statistical techniques (and of the possible traps that they can hide) by using real data in concrete situations drawn from research activity.

This book provides a first introduction to mathematical statistics. The text arose from a series of lectures given at the University of Nijmegen (Holland) and is intended for students who already have some basic mathematical background. The text covers compulsory fundamental topics like estimation theory, sufficiency, hypothesis testing, analysis of variance, and non-parametric methods. Moreover, there are also introductory sections about the Kolmogorov-Smirnov test, von Mises differentiation, influence functions, robustness, metrics on sets of distribution functions, smoothing techniques, bootstrap methods, and density estimation. The final chapters of the book contains a first course in vectorial statistics and multiple regression analysis. As a rule, theorems are proved in a mathematically rigorous way. Many examples and exercises are included. There is an accompanying volume, in which completely worked through solutions to all exercises can be found. Both books are very suitable for self-study.

This book will interest and assist people who are dealing with the problems of predicitons of time series in higher education and research. It will greatly assist people who apply time series theory to practical problems in their work and also serve as a textbook for postgraduate students in statistics economics and related subjects.

Designed to offer an accessible set of case studies and analyses of ethical dilemmas in data science. This book will be suitable for technical readers in data science who want to understand diverse ethical approaches to AI.

Leading biostatisticians and biomedical researchers describe many of the key techniques used to solve commonly occurring data analytic problems in molecular biology, and demonstrate how these methods can be used in the development of new markers for exposure to a risk factor or for disease outcomes. Major areas of application include microarray analysis, proteomic studies, image quantitation, genetic susceptibility and association, evaluation of new biomarkers, and power analysis and sample size.

The choice of examples used in this text clearly illustrate its use for a one-year graduate course. The material to be presented in the classroom constitutes a little more than half the text, while the rest of the text provides background, offers different routes that could be pursued in the classroom, as well as additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Steins method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function, with both the bootstrap and trimming presented. The section on martingales covers censored data martingales.

Since Efron's profound paper on the bootstrap, an enormous amount of effort has been spent on the development of bootstrap, jacknife, and other resampling methods. The primary goal of these computer-intensive methods has been to provide statistical tools that work in complex situations without imposing unrealistic or unverifiable assumptions about the data generating mechanism. This book sets out to lay some of the foundations for subsampling methodology and related methods.

This volume presents selected peer-reviewed contributions from The International Work-Conference on Time Series, ITISE 2015, held in Granada, Spain, July 1-3, 2015. It discusses topics in time series analysis and forecasting, advanced methods and online learning in time series, high-dimensional and complex/big data time series as well as forecasting in real problems. The International Work-Conferences on Time Series (ITISE) provide a forum for scientists, engineers, educators and students to discuss the latest ideas and implementations in the foundations, theory, models and applications in the field of time series analysis and forecasting. It focuses on interdisciplinary and multidisciplinary research encompassing the disciplines of computer science, mathematics, statistics and econometrics.

Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other. This book is meant to help the reader understand and relate algorithms to each other in some intuitive fashion, and represents, in this respect, a consolidation of the field. The framework of algorithms presented in this book is called Cost Approxi mation. (The preface of the Ph.D. thesis Pat93d] explains the background to the work that lead to the thesis, and ultimately to this book.) It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the update of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of this book is to offer this framework as an intuitively appeal ing tool for describing an algorithm. One of the advantages of the framework, or any reasonable framework for that matter, is that two algorithms may be easily related and compared through its use. This framework is particular in that it covers a vast number of methods, while still being fairly detailed; the level of abstraction is in fact the same as that of the original problem statement."

This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance. This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.

This book presents Explainable Artificial Intelligence (XAI), which aims at producing explainable models that enable human users to understand and appropriately trust the obtained results. The authors discuss the challenges involved in making machine learning-based AI explainable. Firstly, that the explanations must be adapted to different stakeholders (end-users, policy makers, industries, utilities etc.) with different levels of technical knowledge (managers, engineers, technicians, etc.) in different application domains. Secondly, that it is important to develop an evaluation framework and standards in order to measure the effectiveness of the provided explanations at the human and the technical levels. This book gathers research contributions aiming at the development and/or the use of XAI techniques in order to address the aforementioned challenges in different applications such as healthcare, finance, cybersecurity, and document summarization. It allows highlighting the benefits and requirements of using explainable models in different application domains in order to provide guidance to readers to select the most adapted models to their specified problem and conditions. Includes recent developments of the use of Explainable Artificial Intelligence (XAI) in order to address the challenges of digital transition and cyber-physical systems; Provides a textual scientific description of the use of XAI in order to address the challenges of digital transition and cyber-physical systems; Presents examples and case studies in order to increase transparency and understanding of the methodological concepts.

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. This book is devoted to stochastic operators in Hilbert space. A number of models in modern probability theory apply the notion of a stochastic operator in explicit or latent form. In this book, objects from the Gaussian case are considered. Therefore, it is useful to consider all random variables and elements as functionals from the Wiener process or its formal derivative, i.e. white noise. The book consists of five chapters. The first chapter is devoted to stochastic calculus and its main goal is to prepare the tools for solving stochastic equations. In the second chapter the structure of stochastic equations, mainly the structure of Gaussian strong linear operators, is studied. In chapter 3 the definition of the action of the stochastic operator on random elements in considered. Chapter 4 deals with the mathematical models in which the notions of stochastic calculus arise and in the final chapter the equation with random operators is considered.

This book illustrates numerous statistical practices that are commonly used by medical researchers, but which have severe flaws that may not be obvious. For each example, it provides one or more alternative statistical methods that avoid misleading or incorrect inferences being made. The technical level is kept to a minimum to make the book accessible to non-statisticians. At the same time, since many of the examples describe methods used routinely by medical statisticians with formal statistical training, the book appeals to a broad readership in the medical research community.

Self-contained chapters on the most important applications and methodologies in finance, which can easily be used for the reader’s research or as a reference for courses on empirical finance. Each chapter is reproducible in the sense that the reader can replicate every single figure, table, or number by simply copy-pasting the code we provide. A full-fledged introduction to machine learning with tidymodels based on tidy principles to show how factor selection and option pricing can benefit from Machine Learning methods. Chapter 2 on accessing & managing financial data shows how to retrieve and prepare the most important datasets in the field of financial economics: CRSP and Compustat. The chapter also contains detailed explanations of the most important data characteristics. Each chapter provides exercises that are based on established lectures and exercise classes and which are designed to help students to dig deeper. The exercises can be used for self-studying or as source of inspiration for teaching exercises.

Provides a comprehensive and accessible introduction to general insurance pricing, based on the author’s many years of experience as both a teacher and practitioner. Suitable for students taking a course in general insurance pricing, notably if they are studying to become an actuary through the UK Institute of Actuaries exams. No other title quite like this on the market that is perfect for teaching/study, and is also an excellent guide for practitioners.

This volume contains the text of the twenty-five papers presented at two workshops entitled Maximum-Entropy and Bayesian Methods in Applied Statistics, which were held at the University of Wyoming from June 8 to 10, 1981, and from August 9 to 11, 1982. The workshops were organized to bring together researchers from different fields to critically examine maxi mum-entropy and Bayesian methods in science, engineering, medicine, oceanography, economics, and other disciplines. An effort was made to maintain an informal environment where ideas could be easily ~xchanged. That the workshops were at least partially successful is borne out by the fact that there have been two succeeding workshops, and the upcoming Fifth Workshop promises to be the largest of all. These workshops and their proceedings could not have been brought to their final form without the substantial help of a number of people. The support of David Hofmann, the past chairman, and Glen Rebka, Jr. , the present chairman of the Physics Department of the University of Wyoming, has been strong and essential. Glen has taken a special interest in seeing that the proceedings have received the support required for their comple tion. The financial support of the Office of University Research Funds, University of Wyoming, is gratefully acknowledged. The secretarial staff, in particular Evelyn Haskell, Janice Gasaway, and Marce Mitchum, of the University of Wyoming Physics Department has contributed a great number of hours in helping C. Ray Smith organize and direct the workshops.

The author has attempted to present a book that provides a non-technical introduction into the area of non-parametric density and regression function estimation. The application of these methods is discussed in terms of the S computing environment. Smoothing in high dimensions faces the problem of data sparseness. A principal feature of smoothing, the averaging of data points in a prescribed neighborhood, is not really practicable in dimensions greater than three if we have just one hundred data points. Additive models provide a way out of this dilemma; but, for their interactiveness and recursiveness, they require highly effective algorithms. For this purpose, the method of WARPing (Weighted Averaging using Rounded Points) is described in great detail.