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This study guide is designed for students taking courses in engineering mathematics and mathematical methods in science. The textbook includes problems with detailed solutions to teach students the subjects in detail and partially and fully solved exercises with hints to required formulas and answers, enabling students to practice independently and guiding them through problem-solving procedures. The material covered in the book includes complex functions, complex transformations, singularities of complex functions, complex series, Taylor and Laurent series expansions, residue, complex integration, Fourier series, half-domain Fourier sine and cosine series, complex Fourier series, Fourier integral, complex Fourier integral, Fourier transform, half-domain Fourier sine and cosine transform, and partial differential equations. Offering detailed solutions, multiple problem-solving methods, and clear explanations of concepts, this hands-on tutorial will improve students'problem-solving skills and foster a solid understanding of engineering mathematics and mathematical methods in science.

This first comprehensive book on models behind Generative AI has been thoroughly revised to cover all major classes of deep generative models: mixture models, Probabilistic Circuits, Autoregressive Models, Flow-based Models, Latent Variable Models, GANs, Hybrid Models, Score-based Generative Models, Energy-based Models, and Large Language Models. In addition, Generative AI Systems are discussed, demonstrating how deep generative models can be used for neural compression, among others. Deep Generative Modeling is designed to appeal to curious students, engineers, and researchers with a modest mathematical background in undergraduate calculus, linear algebra, probability theory, and the basics of machine learning, deep learning, and programming in Python and PyTorch (or other deep learning libraries). It should find interest among students and researchers from a variety of backgrounds, including computer science, engineering, data science, physics, and bioinformatics who wish to get familiar with deep generative modeling. In order to engage with a reader, the book introduces fundamental concepts with specific examples and code snippets. The full code accompanying the book is available on the author's GitHub site: github.com/jmtomczak/intro_dgm The ultimate aim of the book is to outline the most important techniques in deep generative modeling and, eventually, enable readers to formulate new models and implement them.

This book deals with extreme value theory for univariate and multivariate time series models characterized by power-law tails. These include the classical ARMA models with heavy-tailed noise and financial econometrics models such as the GARCH and stochastic volatility models. Rigorous descriptions of power-law tails are provided through the concept of regular variation. Several chapters are devoted to the exploration of regularly varying structures. The remaining chapters focus on the impact of heavy tails on time series, including the study of extremal cluster phenomena through point process techniques. A major part of the book investigates how extremal dependence alters the limit structure of sample means, maxima, order statistics, sample autocorrelations. This text illuminates the theory through hundreds of examples and as many graphs showcasing its applications to real-life financial and simulated data. The book can serve as a text for PhD and Master courses on applied probability, extreme value theory, and time series analysis. It is a unique reference source for the heavy-tail modeler. Its reference quality is enhanced by an exhaustive bibliography, annotated by notes and comments making the book broadly and easily accessible.

The Volume 1 book on Accelerating Discoveries in Data Science and Artificial Intelligence (Proceedings of ICDSAI 2023), that was held on April 24-25, 2023 by CSUSB USA, the International Association of Academicians (IAASSE), and the Lendi Institute of Engineering and Technology, Vizianagaram, India is intended to be used as a reference book for researchers and practitioners in the disciplines of AI and data science. The book introduces key topics and algorithms and explains how these contribute to healthcare, manufacturing, law, finance, retail, real estate, accounting, digital marketing, and various other fields. The book is primarily meant for academics, researchers, and engineers who want to employ data science techniques and AI applications to address real-world issues. Besides that, businesses and technology creators will also find it appealing to use in industry.

This volume provides a comprehensive survey that covers various modern methods used for detecting and estimating change points in time series and their models. The book primarily focuses on asymptotic theory and practical applications of change point analysis. The methods discussed in the book go beyond the traditional change point methods for univariate and multivariate series. It also explores techniques for handling heteroscedastic series, high-dimensional series, and functional data. While the primary emphasis is on retrospective change point analysis, the book also presents sequential'on-line'methods for detecting change points in real-time scenarios. Each chapter in the book includes multiple data examples that illustrate the practical application of the developed results. These examples cover diverse fields such as economics, finance, environmental studies, and health data analysis. To reinforce the understanding of the material, each chapter concludes with several exercises.Additionally, the book provides a discussion of background literature, allowing readers to explore further resources for in-depth knowledge on specific topics. Overall,'Change Point Analysis for Time Series'offers a broad and informative overview of modern methods in change point analysis, making it a valuable resource for researchers, practitioners, and students interested in analyzing and modeling time series data.

This book, using R and RStudio, demonstrates how to render an audit opinion that is legally and statistically defensible; analyze, extract, and manipulate accounting data; build a risk assessment matrix to inform the conduct of a cost-effective audit program; and more. Today, information technology plays a pivotal role in financial control and audit: most financial data is now digitally recorded and dispersed among servers, clouds and networks over which the audited firm has no control. Additionally, a firm's data—particularly in the case of finance, software, insurance and biotech firms—comprises most of the audited value of the firm. Financial audits are critical mechanisms for ensuring the integrity of information systems and the reporting of organizational finances. They help avoid the abuses that led to passage of legislation such as the Foreign Corrupt Practices Act (1977), and the Sarbanes-Oxley Act (2002). Audit effectiveness has declined over the past two decades, as auditor skillsets have failed to keep up with advances in information technology. Information and communication technology lie at the core of commerce today and are integrated in business processes around the world. This book is designed to meet the increasing need of audit professionals to understand information technology and the controls required to manage it. This 2nd edition includes updated code and test. Machine learning, AI, and SEC's EDGAR data are also, improved and updated. The material included focuses on the requirements for annual Securities and Exchange Commission audits (10-K) for listed corporations. These represent the benchmark auditing procedures for specialized audits, such as internal, governmental, and attestation audits. Many examples reflect the focus of the 2024 CPA exam, and the data analytics-machine learning approach will be central to the AICPA's programs, in the near future.

This book presents a thoughtful compilation of chapters derived from the proceedings of the 8th International Arab Conference on Mathematics and Computations (IACMC 2023), held at Zarqa University in Zarqa, Jordan, from 10–12 May 2023. Encompassing a broad spectrum of themes crucial to contemporary research and development, the book delved into subjects ranging from partial and differential equations to fractional calculus, from probability and statistics to graph theory, and from approximation theory to nonlinear dynamics. Moreover, it explores pivotal areas such as numerical analysis and methods, as well as fostering interdisciplinary mathematical research initiatives. Building upon the legacy of its predecessors, IACMC 2023 served as a premier platform for scholars, researchers and industry professionals to converge and exchange insights on a myriad of cutting-edge advancements and practical applications within the realm of mathematical sciences. This volume encapsulates the essence of IACMC 2023, offering readers a comprehensive overview of the latest breakthroughs and trends in mathematical sciences while serving as a testament to the collaborative spirit and intellectual vigor that define this esteemed conference series.

This book is about how statistics play a role in life, whether in business, psychology, biology, economics, or just about anything short of basket weaving. You cannot make a trip to the doctor, watch a football game, or even go to the grocery store without some statistic staring you down. Your age, weight, and cholesterol make you a high risk for diabetes … the chance that your team will win the game is 12.5 percent … 4 out of 5 dentists like this toothpaste. What does it all mean? Adventures in Statistics: How We Live in a World of Numbers tells you what all those numbers mean. But the book does not spit out a bunch of mathematical formulas; the book tells stories. Stories that explain statistics through popular culture, sports, and history. You're confused about that false positive warning in that drug commercial, the 2007 comedy Juno explains how medical tests – including pregnancy tests – fail and why. Not clear about what your coworkers are talking about when they say, ‘black swans.'the 1997 blockbuster Titanic makes sense of the concept. Adventures in Statistics: How We Live in a World of Numbers shows how professionals in medicine, business, politics, sports, and many other fields use numbers. So, just about everyone would gain from reading this book, perhaps even basket weavers.

This book introduces empirical methods for machine learning with a special focus on applications in natural language processing (NLP) and data science. The authors present problems of validity, reliability, and significance and provide common solutions based on statistical methodology to solve them. The book focuses on model-based empirical methods where data annotations and model predictions are treated as training data for interpretable probabilistic models from the well-understood families of generalized additive models (GAMs) and linear mixed effects models (LMEMs). Based on the interpretable parameters of the trained GAMs or LMEMs, the book presents model-based statistical tests such as a validity test that allows for the detection of circular features that circumvent learning. Furthermore, the book discusses a reliability coefficient using variance decomposition based on random effect parameters of LMEMs. Lastly, a significance test based on the likelihood ratios of nested LMEMs trained on the performance scores of two machine learning models is shown to naturally allow the inclusion of variations in meta-parameter settings into hypothesis testing, and further facilitates a refined system comparison conditional on properties of input data. The book is self-contained with an appendix on the mathematical background of generalized additive models and linear mixed effects models as well as an accompanying webpage with the related R and Python code to replicate the presented experiments. The second edition also features a new hands-on chapter that illustrates how to use the included tools in practical applications.

This book introduces probabilistic modelling and explores its role in solving a broad spectrum of engineering problems that arise in Information Technology (IT). Divided into three parts, it begins by laying the foundation of basic probability concepts such as sample space, events, conditional probability, independence, total probability law and random variables. The second part delves into more advanced topics including random processes and key principles like Maximum A Posteriori (MAP) estimation, the law of large numbers and the central limit theorem. The last part applies these principles to various IT domains like communication, social networks, speech recognition, and machine learning, emphasizing the practical aspect of probability through real-world examples, case studies, and Python coding exercises. A notable feature of this book is its narrative style, seamlessly weaving together probability theories with both classical and contemporary IT applications. Each concept is reinforced with tightly-coupled exercise sets, and the associated fundamentals are explored mostly from first principles. Furthermore, it includes programming implementations of illustrative examples and algorithms, complemented by a brief Python tutorial. Departing from traditional organization, the book adopts a lecture-notes format, presenting interconnected themes and storylines. Primarily tailored for sophomore-level undergraduates, it also suits junior and senior-level courses. While readers benefit from mathematical maturity and programming exposure, supplementary materials and exercise problems aid understanding. Part III serves to inspire and provide insights for students and professionals alike, underscoring the pragmatic relevance of probabilistic concepts in IT.

The two-volume set LNBIP 518 and 519 constitutes the refereed post-conference proceedings of the 25th International Conference on Enterprise Information Systems, ICEIS 2023, which was held in Prague, Czech Republic, during April 2023. The 30 full papers included in these proceedings were carefully reviewed and selected from a total of 213 submissions. They are organized in topical sections as follows: Part One : Databases and Information Systems Integration; Artificial Intelligence and Decision Support Systems; and Information Systems Analysis and Specification. Part Two : Software Agents and Internet Computing; Human-Computer Interaction; and Enterprise Architecture.

This two-volume set constitutes the refereed post-conference proceedings of the 25th International Conference on Enterprise Information Systems, ICEIS 2023, which was held in Prague, Czech Republic, during April 2023. The 41 full papers and 66 short papers presented were carefully reviewed and selected from 213 submissions. They are organized in topical sections as follows: Part One : Databases and Information Systems Integration; Artificial Intelligence and Decision Support Systems; and Information Systems Analysis and Specification. Part Two : Software Agents and Internet Computing; Human-Computer Interaction; and Enterprise Architecture.

An applied introduction to probability and statistics, now in a practical, digital eBook format. For a one- or two-semester course; calculus background presumed, no previous study of probability or statistics is required. Probability and Statistical Inference, Global Edition is written by three veteran statisticians, emphasising the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variation. Designed for students with a background in calculus, this book continues to reinforce basic mathematical concepts, with numerous real-world examples and applications to illustrate the relevance of key concepts. The full text downloaded to your computer With eBooks you can: search for key concepts, words and phrases make highlights and notes as you study share your notes with friends eBooks are downloaded to your computer and accessible either offline through the Bookshelf (available as a free download), available online and also via the iPad and Android apps. Upon purchase, you'll gain instant access to this eBook. Time limit The eBooks products do not have an expiry date. You will continue to access your digital ebook products whilst you have your Bookshelf installed.

This book presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and covers numerical linear algebra. Matrix algebra is one of the most important areas of mathematics in data science and in statistical theory, and previous editions had essential updates and comprehensive coverage on critical topics in mathematics.This 3rd edition offers a self-contained description of relevant aspects of matrix algebra for applications in statistics. It begins with fundamental concepts of vectors and vector spaces; covers basic algebraic properties of matrices and analytic properties of vectors and matrices in multivariate calculus; and concludes with a discussion on operations on matrices, in solutions of linear systems and in eigenanalysis. It also includes discussions of the R software package, with numerous examples and exercises.Matrix Algebra considers various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes special properties of those matrices; as well as describing various applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. It begins with a discussion of the basics of numerical computations and goes on to describe accurate and efficient algorithms for factoring matrices, how to solve linear systems of equations, and the extraction of eigenvalues and eigenvectors. It covers numerical linear algebra—one of the most important subjects in the field of statistical computing. The content includes greater emphases on R, and extensive coverage of statistical linear models. Matrix Algebra is ideal for graduate and advanced undergraduate students, or as a supplementary text for courses in linear models or multivariate statistics. It's also ideal for use in a course in statistical computing, or as a supplementary text forvarious courses that emphasize computations.

This book focuses on correlation coefficients and its applications in applied science fields. The book begins by describing the historical development and various types of correlations. Rank correlation methods including Pearson's, Spearman's, and Kendall's correlation are discussed at length. The book also discusses sampling distribution of correlation coefficients and applications of correlations in various fields. The book presents novel topics such as (i) a quick analytical method to approximate Pearson's correlation, (ii) single-variable correlation, (iii) fractional co-skewness and co-kurtosis, and (iv) the fallacy on correlation between the sample mean and sample variance. This book is ideal for courses on mathematical statistics, engineering statistics, and exploratory data analysis and is primarily aimed at upper-undergraduate and graduate level students. The book is also useful for researchers and professionals in various fields who are interested in data analysis.

This book provides a self-contained introduction to a new class of stochastic models for systems of spiking neurons. These systems have a large number of interacting components, each one evolving as a stochastic process with a memory of variable length. Several mathematical tools are put to use, such as Markov chains, stochastic chains having memory of variable length, point processes having stochastic intensity, Hawkes processes, random graphs, mean field limits, perfect sampling algorithms, the Context algorithm, and statistical model selection.The book's focus on mathematically tractable objects distinguishes it from other texts on theoretical neuroscience. The biological complexity of neurons is not ignored, but reduced to some of its main features, such as the intrinsic randomness of neuronal dynamics. This reduction in complexity aims at explaining and reproducing statistical regularities and collective phenomena that are observed in experimental data, an approach that leads to mathematically rigorous results. With an emphasis on a constructive and algorithmic point of view, this book is directed towards mathematicians interested in learning about stochastic network models and their neurobiological underpinning, and neuroscientists interested in learning how to build and prove results with mathematical models that relate to actual experimental settings.

This book constitutes the refereed proceedings of the 17th International Conference on Simulation of Adaptive Behavior, SAB 2024, held in Irvine, CA, USA, during September 9–12, 2024. The 26 full papers included in this book were carefully reviewed and selected from 30 submissions. They were organized in topical sections as follows: Bio-Inspired Navigation; Biomimetic Robots; Collective Behavior; Evolutionary Approaches to Adaptive Behavior; Motor Learning and Problem Solving and Decision-Making.

This book constitutes the refereed proceedings of the 2nd International Conference, ITMM 2023 and 14th International Workshop, WRQ 2023, held in Tomsk, Russia, during December 4–9, 2023. The 23 full papers included in this book were carefully reviewed and selected from 96 submissions. The papers are devoted to new results in queueing theory and its applications, and also related areas of probabilistic analysis. Its target audience includes specialists in probabilistic theory, random processes, and mathematical modeling as well as engineers engaged in logical and technical design and operational management of data processing systems, communication, and computer networks.

The book is about the development of the theory of epistemic fields with the corresponding relational and information fields as a framework for the understanding of strategies and tactics of the theory of knowing as the production of intellectual investment flows and the theory of knowledge accumulation as the production of intellectual capital stocks in systems of factories and departments providing the foundations for the development of open algorithms in the open space of problem-solution dualities. The concepts and the roles of thinking and reasoning with curiosity, creativity, hope, Ill-posed problems, phantom problems, unsolved problems, misinformation, disinformation, fake news, and courage are introduced, defined, and analyzed on the cognitive journeys over the space of ignorance-knowledge dualities, where dualistic-polar conflicts between duals in the space of ignorance-knowledge dualities are resolved with the instruments of fuzzy optimization, the results of which are used to induced the zones of ignorance, the zones of knowledge, and the zones of contentions. A complete development of the set of connecting paths of spaces and sub-spaces is provided, where all varieties, categories, and spaces reside in dualistic-polar structures with knowledge stock viewed as a single tree with the same roots, one trunk, many branches, and a fruit cocktail. The ontological space contains the space of actual-potential dualities as the primary category of knowing, and the epistemological space contains the space of imagination-reality dualities as the derived category of knowing within the space of primary-derived dualities. The space of potentials contains the space of imaginations which contains the sub-spaces of possibility-impossibility, probability-improbability, and possibility-probability dualities with corresponding spaces of necessity-freedom and anticipation-expectation dualities leading to the conception of the possible-world-impossible-world dualities in the space of semantic-non-semantic dualities. This book is also a continuation of the sequence of my works on the theories of paradigms of thought, rationality, info-statics, info-dynamics, entropy, problem-solution dualities in self-contained mathematics and philosophy, and their relational connectivity to information, language, knowing, knowledge, cognitive practices and open maching learning relative to nominalism, and the space of construction-reduction dualities over the spaces of fundamental-applied, production-consumption, input-output, and cost-benefit dualities.

This book constitutes the refereed proceedings of the 28th International Conference on Analytical and Stochastic Modelling Techniques and Applications, ASMTA 2024, held in Venice, Italy, on June 14, 2024. The 10 full papers presented were carefully reviewed and selected from 14 submissions. These papers covered a wide range of topics in analytical and stochastic modeling techniques and their applications.

This book offers a broad selection of statistical applications to everyday situations, illustrating how exciting and diverse statistical analysis can be. It covers a wide variety of topics, including offering hearing-impaired people the option to enjoy music, extracting meaningful quantitative data from texts, and modeling flood disasters to help get a better grip on them. Most of the examples are not typically found in textbooks but directly relate to real-life problems encountered by the “average person”, including topics relevant for sustainable development.Technical jargon and formalism have been avoided as much as possible, and a detailed statistical background is not assumed of the reader, making the book accessible to anyone interested in current research in statistical applications. Providing an unobscured look at a thoroughly fascinating science, it will help students to develop enthusiasm for statistical issues and methods, and may even inspire ideas for their own projects.

​This book constitutes the proceedings of the 14th International Workshop on Statistical Atlases and Computational Models of the Heart, STACOM 2023, as well as the Cardiac MRI Reconstruction Challenge, CMRxRecon Challenge. There was a total of 53 submissions to the workshop. The 24 regular workshop papers included in this volume were carefully reviewed and selected from 29 paper submissions. They deal with cardiac segmentation, modelling, strain quantification, registration, statistical shape analysis, and quality control. In addition, 21 papers from the CMRxRecon challenge are included in this volume. They focus on fast CMR image reconstruction and provide a benchmark dataset that enables the broader research community to promote advances in this area of research.

This volume presents a unique collection of original research contributions by leading experts in several modern fields of econometrics and statistics, including high-dimensional, nonparametric and robust statistics, time series analysis and factor models. Published in honour of Marc Hallin on the occasion of his 75th birthday, it puts emphasis on the fundamental and applied topics he has significantly contributed to. The volume starts with an annotated bibliography that mainly catalogues his contributions to distribution-free rank-based and quantile-oriented inference and to time series analysis. The main part of the book collects 29 authoritative contributions by some of Marc Hallin's main collaborators, organized into six parts: rank- and depth-based methods, asymptotic statistics, quantile regression, econometrics, statistical modelling and related topics, and high-dimensional and non-Euclidean data.

This book explains the importance of using the probability that the hypothesis is correct (PHC), an intuitive measure that anyone can understand, as an alternative to the p-value. In order to overcome the “reproducibility crisis” caused by the misuse of significance tests, this book provides a detailed explanation of the mechanism of p-hacking using significance tests, and concretely shows the merits of PHC as an alternative to p-values. In March 2019, two impactful papers on statistics were published. One paper,'Moving to a World Beyond ‘p < 0.05'”, was featured in the scholarly journal The American Statistician, overseen by the American Statistical Association. The title of the first chapter is “Don't Say ‘Statistically Significant'”, and it uses the imperative form to clearly forbid the use of significance testing. Another paper, “Retire statistical significance”, was published in the prestigious scientific journal Nature. This commentary was endorsed by more than 800 scientists, advocating for the statement, “We agree, and call for the entire concept of statistical significance to be abandoned.” Consider a study comparing the duration of hospital stays between treatments A and B. Previously, research conclusions were typically stated as: “There was a statistically significant difference at the 5% level in the average duration of hospital stays.” This phrasing is quite abstract. Instead, we present the following conclusion as an example: (1) The average duration of hospital stays for Group A is at least half a day shorter than for Group B. (2) 71% of patients in Group A have shorter hospital stays than the average for Group B. (3) Group A has an average hospital stay that is, on average, no more than 94% of that of Group B. Then, the probability that the expression is correct is shown. That is the PHC curve.

This book offers a gentle yet rigorous introduction to probability theory, with a special focus on finite probability spaces. Drawing inspiration from card games, casino games, mahjong, and two-up, it also delves into real-world applications such as weather forecasting, lotteries, hereditary diseases, and PCR virus testing. Discover which casino game gives you the best chance of winning and which one offers the worst odds. Assuming only a high school mathematics background, this book is an excellent resource for both students and teachers, providing clear explanations and engaging examples. The technical material is lightened with entertaining stories, such as how someone became a millionaire by spotting a flaw in a national lottery and how another person helped fund a war using winnings from a well-known card game he invented. Engaging and informative, this book is perfect for anyone looking to deepen their understanding of probability theory while enjoying some fascinating anecdotes along the way.

This textbook reconstructs the statistics curriculum from the perspective of posterior probability. In recent years, there have been several reports that the results of studies using significant tests cannot be reproduced. It is a problem called a “reproducibility crisis”. For example, suppose we could reject the null hypothesis that “the average number of days to recovery in patients who took a new drug was the same as that in the control group”. However, rejecting the null hypothesis is only a necessary condition for the new drug to be effective. Even if the necessary conditions are met, it does not necessarily mean that the new drug is effective. In fact, there are many cases where the effect is not reproduced. Sufficient conditions should be presented, such as “the average number of days until recovery in patients who take new drugs is sufficiently short compared to the control group, evaluated from a medical point of view”, without paying attention to necessary conditions. This book reconstructs statistics from the perspective of PHC, i.e., probability that a research hypothesis is correct. For example, the PHC curve shows the posterior probability that the statement “The average number of days until recovery for patients taking a new drug is at least θ days shorter than that of the control group” is correct as a function of θ. Using the PHC curve makes it possible to discuss the sufficient conditions rather than the necessary conditions for being an efficient treatment. The value of statistical research should be evaluated with concrete indicators such as “90% probability of being at least 3 days shorter”, not abstract metrics like the p-value.

This volume on the latest developments in statistical modelling is a collection of refereed papers presented at the 38th International Workshop on Statistical Modelling, IWSM 2024, held from 14 to 19 July 2024 in Durham, UK. The contributions cover a wide range of topics in statistical modelling, including generalized linear models, mixture models, regularization techniques, hidden Markov models, smoothing methods, censoring and imputation techniques, Gaussian processes, spatial statistics, shape modelling, goodness-of-fit problems, and network analysis. Various highly topical applications are presented as well, especially from biostatistics. The approaches are equally frequentist and Bayesian, a categorization the statistical modelling community has synergetically overcome. The book also features the workshop's keynote contribution on statistical modelling for big and little data, highlighting that both small and large data sets come with their own challenges. The International Workshop on Statistical Modelling (IWSM) is the annual workshop of the Statistical Modelling Society, with the purpose of promoting important developments, extensions, and applications in statistical modelling, and bringing together statisticians working on related problems from various disciplines. This volume reflects this spirit and contributes to initiating and sustaining discussions about problems in statistical modelling and triggers new developments and ideas in the field.

A strong grasp of elementary statistics and probability, along with basic skills in using R, is essential for various scientific disciplines reliant on data analysis. This book serves as a gateway to learning statistical methods from scratch, assuming a solid background in high school mathematics. Readers gradually progress from basic concepts to advanced statistical modelling, with examples from actuarial, biological, ecological, engineering, environmental, medicine, and social sciences highlighting the real-world relevance of the subject. An accompanying R package enables seamless practice and immediate application, making it ideal for beginners. The book comprises 19 chapters divided into five parts. Part I introduces basic statistics and the R software package, teaching readers to calculate simple statistics and create basic data graphs. Part II delves into probability concepts, including rules and conditional probability, and introduces widelyused discrete and continuous probability distributions (e.g., binomial, Poisson, normal, log-normal). It concludes with the central limit theorem and joint distributions for multiple random variables. Part III explores statistical inference, covering point and interval estimation, hypothesis testing, and Bayesian inference. This part is intentionally less technical, making it accessible to readers without an extensive mathematical background. Part IV addresses advanced probability and statistical distribution theory, assuming some familiarity with (or concurrent study of) mathematical methods like advanced calculus and linear algebra. Finally, Part V focuses on advanced statistical modelling using simple and multiple regression and analysis of variance, laying the foundation for further studies in machine learning and data science applicable to various data and decision analytics contexts. Based on years of teaching experience, this textbook includes numerousexercises and makes extensive use of R, making it ideal for year-long data science modules and courses. In addition to university courses, the book amply covers the syllabus for the Actuarial Statistics 1 examination of the Institute and Faculty of Actuaries in London. It also provides a solid foundation for postgraduate studies in statistics and probability, or a reliable reference for statistics.

Mobile crowdsensing (MCS) is emerging as a novel sensing paradigm in the Internet of Things (IoTs) due to the proliferation of smart devices (e.g., smartphones, wearable devices) in people's daily lives. These ubiquitous devices provide an opportunity to harness the wisdom of crowds by recruiting mobile users to collectively perform sensing tasks, which largely collect data about a wide range of human activities and the surrounding environment. However, users suffer from resource consumption such as battery, processing power, and storage, which discourages users'participation. To ensure the participation rate, it is necessary to employ an incentive mechanism to compensate users'costs such that users are willing to take part in crowdsensing. This book sheds light on the design of incentive mechanisms for MCS in the context of game theory. Particularly, this book presents several game-theoretic models for MCS in different scenarios. In Chapter 1, the authors present an overview of MCS and state the significance of incentive mechanism for MCS. Then, in Chapter 2, 3, 4, and 5, the authors propose a long-term incentive mechanism, a fair incentive mechanism, a collaborative incentive mechanism, and a coopetition-aware incentive mechanism for MCS, respectively. Finally, Chapter 6 summarizes this book and point out the future directions. This book is of particular interest to the readers and researchers in the field of IoT research, especially in the interdisciplinary field of network economics and IoT.

This book presents an up-to-date perspective on randomized response techniques (RRT). It discusses the most appropriate and efficient procedures of RRT for analysing data from queries dealing with sensitive and confidential issues, including the treatment of infinite and finite population setups. The book aims to spark a renewed interest among sampling experts who may have overlooked RRT. By addressing the missing topics and incorporating a wide range of contributors'works, it seeks to foster an appreciative academic environment and inspire a reformed and amended view of RRT. As the book unfolds, readers will gain valuable insights into the evolving landscape of RRT and its applications, positioning them at the forefront of this engaging field of study.On RRT, the literature has grown immensely since its inception in 1965 by S.L. Warner. Despite several books published on the subject, there are still two crucial topics missing from the existing RRT literature. This book aimsto address these gaps and provide valuable insights to curious readers in the field. The book is mandatory reading for statisticians and biostatisticians, market researchers, operations researchers, pollsters, sociologists, political scientists, economists and advanced undergraduate and graduate students in these areas.

This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.

A nontechnical guide to the basic ideas of modern causal inference, with illustrations from health, the economy, and public policy.Which of two antiviral drugs does the most to save people infected with Ebola virus? Does a daily glass of wine prolong or shorten life? Does winning the lottery make you more or less likely to go bankrupt? How do you identify genes that cause disease? Do unions raise wages? Do some antibiotics have lethal side effects? Does the Earned Income Tax Credit help people enter the workforce? Causal Inference provides a brief and nontechnical introduction to randomized experiments, propensity scores, natural experiments, instrumental variables, sensitivity analysis, and quasi-experimental devices. Ideas are illustrated with examples from medicine, epidemiology, economics and business, the social sciences, and public policy.

This book presents a selection of peer-reviewed contributions on the latest developments in time series analysis and forecasting, presented at the 7th International Conference on Time Series and Forecasting, ITISE 2021, held in Gran Canaria, Spain, July 19-21, 2021. It is divided into four parts. The first part addresses general modern methods and theoretical aspects of time series analysis and forecasting, while the remaining three parts focus on forecasting methods in econometrics, time series forecasting and prediction, and numerous other real-world applications. Covering a broad range of topics, the book will give readers a modern perspective on the subject.The ITISE conference series provides a forum for scientists, engineers, educators and students to discuss the latest advances and implementations in the foundations, theory, models and applications of time series analysis and forecasting. It focuses on interdisciplinary research encompassing computer science, mathematics,statistics and econometrics.

This book constitutes the refereed proceedings of the 18th European Workshop on Computer Performance Engineering, EPEW 2022, held in Santa Pola, Spain, in September 2022.The 14 papers presented in this volume together with one invited talk were carefully reviewed and selected from 14 submissions. The papers presented at the workshop reflect the diversity of modern performance engineering. The sessions covered a wide range of topics including robustness analysis, machine learning, edge and cloud computing, as well as more traditional topics on stochastic modelling, techniques and tools.

This book presents a study of statistical inferences based on the kernel-type estimators of distribution functions. The inferences involve matters such as quantile estimation, nonparametric tests, and mean residual life expectation, to name just some. Convergence rates for the kernel estimators of density functions are slower than ordinary parametric estimators, which have root-n consistency. If the appropriate kernel function is used, the kernel estimators of the distribution functions recover the root-n consistency, and the inferences based on kernel distribution estimators have root-n consistency. Further, the kernel-type estimator produces smooth estimation results. The estimators based on the empirical distribution function have discrete distribution, and the normal approximation cannot be improved—that is, the validity of the Edgeworth expansion cannot be proved. If the support of the population density function is bounded, there is a boundary problem, namely the estimator does not have consistency near the boundary. The book also contains a study of the mean squared errors of the estimators and the Edgeworth expansion for quantile estimators.

This book organizes principles and methods of signal processing and machine learning into the framework of coherence. The book contains a wealth of classical and modern methods of inference, some reported here for the first time. General results are applied to problems in communications, cognitive radio, passive and active radar and sonar, multi-sensor array processing, spectrum analysis, hyperspectral imaging, subspace clustering, and related. The reader will find new results for model fitting; for dimension reduction in models and ambient spaces; for detection, estimation, and space-time series analysis; for subspace averaging; and for uncertainty quantification. Throughout, the transformation invariances of statistics are clarified, geometries are illuminated, and null distributions are given where tractable. Stochastic representations are emphasized, as these are central to Monte Carlo simulations. The appendices contain a comprehensive account of matrix theory, the SVD, the multivariate normal distribution, and many of the important distributions for coherence statistics. The book begins with a review of classical results in the physical and engineering sciences where coherence plays a fundamental role. Then least squares theory and the theory of minimum mean-squared error estimation are developed, with special attention paid to statistics that may be interpreted as coherence statistics. A chapter on classical hypothesis tests for covariance structure introduces the next three chapters on matched and adaptive subspace detectors. These detectors are derived from likelihood reasoning, but it is their geometries and invariances that qualify them as coherence statistics. A chapter on independence testing in space-time data sets leads to a definition of broadband coherence, and contains novel applications to cognitive radio and the analysis of cyclostationarity. The chapter on subspace averaging reviews basic results and derives an order-fitting rule for determining the dimension of an average subspace. These results are used to enumerate sources of acoustic and electromagnetic radiation and to cluster subspaces into similarity classes. The chapter on performance bounds and uncertainty quantification emphasizes the geometry of the Cramèr-Rao bound and its related information geometry.

The book equips students with the end-to-end skills needed to do data science. That means gathering, cleaning, preparing, and sharing data, then using statistical models to analyse data, writing about the results of those models, drawing conclusions from them, and finally, using the cloud to put a model into production, all done in a reproducible way.At the moment, there are a lot of books that teach data science, but most of them assume that you already have the data. This book fills that gap by detailing how to go about gathering datasets, cleaning and preparing them, before analysing them. There are also a lot of books that teach statistical modelling, but few of them teach how to communicate the results of the models and how they help us learn about the world. Very few data science textbooks cover ethics, and most of those that do, have a token ethics chapter. Finally, reproducibility is not often emphasised in data science books. This book is based around a straight-forward workflow conducted in an ethical and reproducible way: gather data, prepare data, analyse data, and communicate those findings. This book will achieve the goals by working through extensive case studies in terms of gathering and preparing data, and integrating ethics throughout. It is specifically designed around teaching how to write about the data and models, so aspects such as writing are explicitly covered. And finally, the use of GitHub and the open-source statistical language R are built in throughout the book.Key Features: Extensive code examples. Ethics integrated throughout. Reproducibility integrated throughout. Focus on data gathering, messy data, and cleaning data. Extensive formative assessment throughout.

This book introduces the basic principles underlying the design and analysis of the digital communication systems that have heralded the information revolution. One major goal of the book is to demonstrate the role of the digital communication principles in a wide variety of data science applications, including community detection, computational biology, speech recognition and machine learning. One defining feature of this book is to make an explicit connection between the communication principles and data science problems, as well as to succinctly deliver the “story” of how the communication principles play a role for trending data science applications. All the key “plots” involved in the story are coherently developed with the help of tightly coupled exercise problem sets, and the associated fundamentals are explored mostly from first principles. Another key feature is that it includes programming implementation of a variety of algorithms inspired by fundamentals, together with a brief tutorial of the used programming tools. The implementation is based on Python and TensorFlow. This book does not follow a traditional book-style organization, but is streamlined via a series of lecture notes that are intimately related, centered around coherent storylines and themes. It serves as a textbook mainly for a junior- or senior-level undergraduate course, yet is also suitable for a first-year graduate course. Readers benefit from having a good background in probability and random processes, and basic familiarity with Python. But the background can be supplemented by almost self-contained materials, as well as by numerous exercise problems intended for elaborating on non-trivial concepts. In addition, Part III for data science applications should provide motivation and insights to students and even professional scientists who are interested in the field.

This volume constitutes the papers of the 3rd International Workshop on Active Inference, IWAI 2022, held in Grenoble, France, in conjunction with ECML/PKDD, on September 19, 2022.The 25 revised full papers presented in this book were carefully reviewed and selected from 31 submissions.

確率・統計の理論と応用を，予備知識を前提とせず基礎からわかりやすく述べる．確率法則，統計分布，推定と検定などを豊富な例題をまじえて明快に解説し，さらに新しい統計学の成果である情報量規準AICと時系列解析などの適用例をていねいに説明する．演習問題・解答により徹底理解と応用力が得られる．

This book constitutes the proceedings of the 13th International Workshop on Statistical Atlases and Computational Models of the Heart, STACOM 2022, held in conjunction with the 25th MICCAI conference. The 34 regular workshop papers included in this volume were carefully reviewed and selected after being revised and deal with topics such as: common cardiac segmentation and modelling problems to more advanced generative modelling for ageing hearts, learning cardiac motion using biomechanical networks, physics-informed neural networks for left atrial appendage occlusion, biventricular mechanics for Tetralogy of Fallot, ventricular arrhythmia prediction by using graph convolutional network, and deeper analysis of racial and sex biases from machine learning-based cardiac segmentation. In addition, 14 papers from the CMRxMotion challenge are included in the proceedings which aim to assess the effects of respiratory motion on cardiac MRI (CMR) imaging quality and examine the robustness of segmentation models in face of respiratory motion artefacts. A total of 48 submissions to the workshop was received.

This book constitutes the refereed proceedings of the 17th Ibero-American Conference on Artificial Intelligence, IBERAMIA 2022, held in Cartagena de Indias, Colombia, in November 2022. The 33 full and 4 short papers presented were carefully reviewed and selected from 67 submissions. The papers are organized in the following topical sections: applications of AI; ethics and smart city; green and sustainable AI; machine learning; natural language processing; robotics and computer vision; simulation and forecasting.

This book presents the latest developments in the theory and applications of time series analysis and forecasting. Comprising a selection of refereed papers, it is divided into several parts that address modern theoretical aspects of time series analysis, forecasting and prediction, with applications to various disciplines, including econometrics and energy research. The broad range of topics discussed, including matters of particular relevance for sustainable development, will give readers a modern perspective on the subject.The included contributions were originally presented at the 8th International Conference on Time Series and Forecasting, ITISE 2022, held in Gran Canaria, Spain, June 27-30, 2022. The ITISE conference series provides a forum for scientists, engineers, educators and students to discuss the latest advances and implementations in the foundations, theory, models and applications of time series analysis and forecasting. It focuses on interdisciplinary research encompassing computer science, mathematics, statistics and econometrics.

This book discusses Artificial Neural Networks (ANN) and their ability to predict outcomes using deep and shallow learning principles. The author first describes ANN implementation, consisting of at least three layers that must be established together with cells, one of which is input, the other is output, and the third is a hidden (intermediate) layer. For this, the author states, it is necessary to develop an architecture that will not model mathematical rules but only the action and response variables that control the event and the reactions that may occur within it. The book explains the reasons and necessity of each ANN model, considering the similarity to the previous methods and the philosophical - logical rules.

Computational intelligence consists of those techniques that imitate the human brain and nature to adopt the decision-making approach. This book contains selected papers from the 8th International Conference on Computers, Management and Mathematical Sciences (ICCM) 2022 about fuzzy systems, neural networks and evolutionary computation that can address stochastic environments where reasoning is a significant attribute to derive potential solutions and focus on the business domain's computational aspects.This is a conference proceedings for scholars/students who are using the powerful algorithms, concepts and principles of computational intelligence in a wide spectrum of research cases.

This book describes the probability theory associated with frequently used statistical procedures and the relation between probability theory and statistical inference. The first third of the book is dedicated to probability theory including topics relating to events, random variables, and the Central Limit Theorem. Statistical topics then include parameter estimation with confidence intervals, hypothesis testing, chi-square tests, t tests, and several non-parametric tests. Flow charts are frequently used to facilitate an understanding of the material considered. The examples and problems in the book all concern simple data sets which can be analyzed with a simple calculator; however, the R code required to complete many examples and problems is provided as well for those that are interested.

This book constitutes the refereed proceedings of the 21st International Conference on Information Technologies and Mathematical Modelling. Queueing Theory and Applications, ITMM 2022, held in Karshi, Uzbekistan, during October 25–29, 2022. The 19 full papers included in this book were carefully reviewed and selected from 89 submissions. The papers are devoted to new results in queueing theory and its applications. Its target audience includes specialists in probabilistic theory, random processes, mathematical modeling as well as engineers engaged in logical and technical design and operational management of data processing systems, communication, and computer networks.

This textbook presents an introduction to the mathematical foundations of software engineering. It presents the rich applications of mathematics in areas such as error-correcting codes, cryptography, the safety and security critical fields, the banking and insurance fields, as well as traditional engineering applications. Topics and features: Addresses core mathematics for critical thinking and problem solving Discusses propositional and predicate logic and various proof techniques to demonstrate the correctness of a logical argument. Examines number theory and its applications to cryptography Considers the underlying mathematics of error-correcting codes Discusses graph theory and its applications to modelling networks Reviews tools to support software engineering mathematics, including automated and interactive theorem provers and model checkingDiscusses financial software engineering, including simple and compound interest, probability and statistics, and operations research Discusses software reliability and dependability and explains formal methods used to derive a program from its specification Discusses calculus, matrices, vectors, complex numbers, and quaternions, as well as applications to graphics and robotics Includes key learning topics, summaries, and review questions in each chapter, together with a useful glossary This practical and easy-to-follow textbook/reference is ideal for computer science students seeking to learn how mathematics can assist them in building high-quality and reliable software on time and on budget. The text also serves as an excellent self-study primer for software engineers, quality professionals, and software managers.

As the first book of a three-part series, this book is offered as a tribute to pioneers in vision, such as Béla Julesz, David Marr, King-Sun Fu, Ulf Grenander, and David Mumford. The authors hope to provide foundation and, perhaps more importantly, further inspiration for continued research in vision. This book covers David Marr's paradigm and various underlying statistical models for vision. The mathematical framework herein integrates three regimes of models (low-, mid-, and high-entropy regimes) and provides foundation for research in visual coding, recognition, and cognition. Concepts are first explained for understanding and then supported by findings in psychology and neuroscience, after which they are established by statistical models and associated learning and inference algorithms. A reader will gain a unified, cross-disciplinary view of research in vision and will accrue knowledge spanning from psychology to neuroscience to statistics.

This book discusses the two fundamental elements that underline the science and design of artificial intelligence (AI) systems: the learning and acquisition of knowledge from observational data, and the reasoning of that knowledge together with whatever information is available about the application at hand. It then presents a mathematical treatment of the core issues that arise when unifying first-order logic and probability, especially in the presence of dynamics, including physical actions, sensing actions and their effects. A model for expressing causal laws describing dynamics is also considered, along with computational ideas for reasoning with such laws over probabilistic logical knowledge.