This book discusses diverse concepts and notions - and their applications - concerning probability and random variables at the intermediate to advanced level. It explains basic concepts and results in a clearer and more complete manner than the extant literature. In addition to a range of concepts and notions concerning probability and random variables, the coverage includes a number of key advanced concepts in mathematics. Readers will also find unique results on e.g. the explicit general formula of joint moments and the expected values of nonlinear functions for normal random vectors. In addition, interesting applications of the step and impulse functions in discussions on random vectors are presented. Thanks to a wealth of examples and a total of 330 practice problems of varying difficulty, readers will have the opportunity to significantly expand their knowledge and skills. The book is rounded out by an extensive index, allowing readers to quickly and easily find what they are looking for. Given its scope, the book will appeal to all readers with a basic grasp of probability and random variables who are looking to go one step further. It also offers a valuable reference guide for experienced scholars and professionals, helping them review and refine their expertise.

Statistical learning and analysis techniques have become extremely important today, given the tremendous growth in the size of heterogeneous data collections and the ability to process it even from physically distant locations. Recent advances made in the field of machine learning provide a strong framework for robust learning from the diverse corpora and continue to impact a variety of research problems across multiple scientific disciplines. The aim of this handbook is to familiarize beginners as well as experts with some of the recent techniques in this field.

The Handbook is divided in two sections: Theory and Applications, covering machine learning, data analytics, biometrics, document recognition and security.
very relevant to current research challenges faced in various fieldsself-contained reference to machine learning

emphasis on applications-oriented techniques

The field of statistics not only affects all areas of scientific activity, but also many other matters such as public policy. It is branching rapidly into so many different subjects that a series of handbooks is the only way of comprehensively presenting the various aspects of statistical methodology, applications, and recent developments. The "Handbook of Statistics" is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with Volume 30 dealing with time series. The series is addressed to the entire community of statisticians and scientists in various disciplines who use statistical methodology in their work. At the same time, special emphasis is placed on applications-oriented techniques, with the applied statistician in mind as the primary audience.

Comprehensively presents the various aspects of statistical methodologyDiscusses a wide variety of diverse applications and recent developmentsContributors are internationally renowened experts in their respective areas

How can large bonuses sometimes make CEOs less productive?Why is revenge so important to us?How can confusing directions actually help us?Why is there a difference between what we think will make us happy and what really makes us happy?

In his groundbreaking book, Predictably Irrational, social scientist Dan Ariely revealed the multiple biases that lead us to make unwise decisions. Now, in The Upside of Irrationality, he exposes the surprising negative and positive effects irrationality can have on our lives. Focusing on our behaviors at work and in relationships, he offers new insights and eye-opening truths about what really motivates us on the job, how one unwise action can become a long-term bad habit, how we learn to love the ones we're with, and more. The Upside of Irrationality will change the way we see ourselves at work and at home--and cast our irrational behaviors in a more nuanced light.

Students in the sciences, economics, social sciences, and medicine take an introductory statistics course. And yet statistics can be notoriously difficult for instructors to teach and for students to learn. To help overcome these challenges, Gelman and Nolan have put together this fascinating and thought-provoking book. Based on years of teaching experience the book provides a wealth of demonstrations, activities, examples, and projects that involve active student participation. Part I of the book presents a large selection of activities for introductory statistics courses and has chapters such as 'First week of class'- with exercises to break the ice and get students talking; then descriptive statistics, graphics, linear regression, data collection (sampling and experimentation), probability, inference, and statistical communication. Part II gives tips on what works and what doesn't, how to set up effective demonstrations, how to encourage students to participate in class and to work effectively in group projects. Course plans for introductory statistics, statistics for social scientists, and communication and graphics are provided. Part III presents material for more advanced courses on topics such as decision theory, Bayesian statistics, sampling, and data science.

The use of Bayesian statistics has grown significantly in recent years, and will undoubtedly continue to do so. Applied Bayesian Modelling is the follow-up to the author’s best selling book, Bayesian Statistical Modelling, and focuses on the potential applications of Bayesian techniques in a wide range of important topics in the social and health sciences. The applications are illustrated through many real-life examples and software implementation in WINBUGS – a popular software package that offers a simplified and flexible approach to statistical modelling. The book gives detailed explanations for each example – explaining fully the choice of model for each particular problem. The book

The book provides a good introduction to Bayesian modelling and data analysis for a wide range of people involved in applied statistical analysis, including researchers and students from statistics, and the health and social sciences. The wealth of examples makes this book an ideal reference for anyone involved in statistical modelling and analysis.

This accessible reference includes selected contributions from Bayesian Thinking - Modeling and Computation, Volume 25 in the Handbook of Statistics Series, with a focus on key methodologies and applications for Bayesian models and computation. It describes parametric and nonparametric Bayesian methods for modeling, and how to use modern computational methods to summarize inferences using simulation. The book covers a wide range of topics including objective and subjective Bayesian inferences, with a variety of applications in modeling categorical, survival, spatial, spatiotemporal, Epidemiological, small area and micro array data.

Aids critical thinking on causal effects
Provides simulation based computing techniques
Covers Bioinformatics and Biostatistics

Chance rules our daily lives in many different ways. From the outcomes of the lottery to the outcomes of medical tests, from the basketball court to the court of law. The ways of chance are capricious. Bizarre things happen all the time. Nevertheless, chance has a logic of its own. It obeys the rules of probability. But if you open a standard book on probability, you may very well feel far removed from everyday life. Abstract formulas and mathematical symbols stare back at you with almost every turn of the page.This book introduces you to the logic of chance without the use of mathematical formulas or symbols. In Part One, you will meet the fascinating pioneers of the mathematics of probability, including Galileo Galilei and Blaise Pascal. Their stories will introduce you, step by step, to the basics of probability. In Part Two, various examples in all areas of daily life will show you how chance defies our expectations time and again. But armed with the basic rules of probability and a good dose of inventiveness, you will be able to unravel the counter-intuitive logic of chance.

This book shows that research contributions from different fields-finance, economics, computer sciences, and physics-can provide useful insights into key issues in financial and cryptocurrency markets. Presenting the latest empirical and theoretical advances, it helps readers gain a better understanding of financial markets and cryptocurrencies. Bitcoin was the first cryptocurrency to use a peer-to-peer network to prevent double-spending and to control its issue without the need for a central authority, and it has attracted wide public attention since its introduction. In recent years, the academic community has also started gaining interest in cyptocurrencies, and research in the field has grown rapidly. This book presents is a collection of the latest work on cryptocurrency markets and the properties of those markets. This book will appeal to graduate students and researchers from disciplines such as finance, economics, financial engineering, computer science, physics and applied mathematics working in the field of financial markets, including cryptocurrency markets.

This new handbook contains the most comprehensive account of sample surveys theory and practice to date. It is a second volume on sample surveys, with the goal of updating and extending the sampling volume published as volume 6 of the Handbook of Statistics in 1988. The present handbook is divided into two volumes (29A and 29B), with a total of 41 chapters, covering current developments in almost every aspect of sample surveys, with references to important contributions and available software. It can serve as a self contained guide to researchers and practitioners, with appropriate balance between theory and real life applications.

Each of the two volumes is divided into three parts, with each part preceded by an introduction, summarizing the main developments in the areas covered in that part. Volume29A deals with methods of sample selection and data processing, with the later including editing and imputation, handling of outliers and measurement errors, and methods of disclosure control. The volume contains also a large variety of applications in specialized areas such as household and business surveys, marketing research, opinion polls and censuses. Volume29B is concerned with inference, distinguishing between design-based and model-based methods and focusing on specific problems such as small area estimation, analysis of longitudinal data, categorical data analysis and inference on distribution functions. The volume contains also chapters dealing with case-control studies, asymptotic properties of estimators and decision theoretic aspects.
Comprehensive account of recent developments in sample survey theory and practiceDiscussesa wide variety of diverse applicationsComprehensive bibliography"

This new handbook contains the most comprehensive account of sample surveys theory and practice to date. It is a second volume on sample surveys, with the goal of updating and extending the sampling volume published as volume 6 of the Handbook of Statistics in 1988. The present handbook is divided into two volumes (29A and 29B), with a total of 41 chapters, covering current developments in almost every aspect of sample surveys, with references to important contributions and available software. It can serve as a self contained guide to researchers and practitioners, with appropriate balance between theory and real life applications.

Each of the two volumes is divided into three parts, with each part preceded by an introduction, summarizing the main developments in the areas covered in that part. Volume 1 deals with methods of sample selection and data processing, with the later including editing and imputation, handling of outliers and measurement errors, and methods of disclosure control. The volume contains also a large variety of applications in specialized areas such as household and business surveys, marketing research, opinion polls and censuses. Volume 2 is concerned with inference, distinguishing between design-based and model-based methods and focusing on specific problems such as small area estimation, analysis of longitudinal data, categorical data analysis and inference on distribution functions. The volume contains also chapters dealing with case-control studies, asymptotic properties of estimators and decision theoretic aspects.

Comprehensive account of recent developments in sample survey theory and practice

Covers a wide variety of diverse applications

Comprehensive bibliography

Congruences are ubiquitous in computer science, engineering, mathematics, and related areas. Developing techniques for finding (the number of) solutions of congruences is an important problem. But there are many scenarios in which we are interested in only a subset of the solutions; in other words, there are some restrictions. What do we know about these restricted congruences, their solutions, and applications? This book introduces the tools that are needed when working on restricted congruences and then systematically studies a variety of restricted congruences. Restricted Congruences in Computing defines several types of restricted congruence, obtains explicit formulae for the number of their solutions using a wide range of tools and techniques, and discusses their applications in cryptography, information security, information theory, coding theory, string theory, quantum field theory, parallel computing, artificial intelligence, computational biology, discrete mathematics, number theory, and more. This is the first book devoted to restricted congruences and their applications. It will be of interest to graduate students and researchers across computer science, electrical engineering, and mathematics.

Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry.
This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & Social Sciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.

Economic theories can be expressed in words, numbers, graphs and symbols. The existing traditional economics textbooks cover all four methods, but the general focus is often more on writing about the theory and methods, with few practical examples. With an increasing number of universities having introduced mathematical economics at undergraduate level, Basic mathematics for economic students aims to fill this gap in the field. Basic mathematics for economic students begins with a comprehensive chapter on basic mathematical concepts and methods (suitable for self-study, revision or tutorial purposes) to ensure that students have the necessary foundation. The book is written in an accessible style and is extremely practical. Numerous mathematical economics examples and exercises are provided as well as fully worked solutions using numbers, graphs and symbols. Basic mathematics for economic students is aimed at all economics students. It focuses on quantitative aspects and especially complements the two highly popular theoretical economics textbooks Understanding microeconomics and Understanding macroeconomics, both written by Philip Mohr and published by Van Schaik.

This monograph presents mathematical theory of statistical models described by the essentially large number of unknown parameters, comparable with sample size but can also be much larger. In this meaning, the proposed theory can be called "essentially multiparametric." It is developed on the basis of the Kolmogorov asymptotic approach in which sample size increases along with the number of unknown parameters.
This theory opens a way for solution of central problems of multivariate statistics, which up until now have not been solved. Traditional statistical methods based on the idea of an infinite sampling often break down in the solution of real problems, and, dependent on data, can be inefficient, unstable and even not applicable. In this situation, practical statisticians are forced to use various heuristic methods in the hope the will find a satisfactory solution.
Mathematical theory developed in this book presents a regular technique for implementing new, more efficient versions of statistical procedures. Near exact solutions are constructed for a number of concrete multi-dimensional problems: estimation of expectation vectors, regression and discriminant analysis, and for the solution to large systems of empiric linear algebraic equations. It is remarkable that these solutions prove to be not only non-degenerating and always stable, but also near exact within a wide class of populations.
In the conventional situation of small dimension and large sample size these new solutions far surpass the classical, commonly used consistent ones. It can be expected in the near future, for the most part, traditional multivariate statistical software will be replaced by the always reliable and more efficient versions of statistical procedures implemented by the technology described in this book.
This monograph will be of interest to a variety of specialists working with the theory of statistical methods and its applications. Mathematicians would find new classes of urgent problems to be solved in their own regions. Specialists in applied statistics creating statistical packages will be interested in more efficient methods proposed in the book. Advantages of these methods are obvious: the user is liberated from the permanent uncertainty of possible instability and inefficiency and gets algorithms with unimprovable accuracy and guaranteed for a wide class of distributions.
A large community of specialists applying statistical methods to real data will find a number of always stable highly accurate versions of algorithms that will help them to better solve their scientific or economic problems. Students and postgraduates will be interested in this book as it will help them get at the foremost frontier of modern statistical science.
- Presents original mathematical investigations
and open a new branch of mathematical statistics
- Illustrates a technique for developing always stable and efficient versions of multivariate statistical analysis for large-dimensional problems
- Describes the most popular methods some near exact solutions; including algorithms of non-degenerating large-dimensional discriminant and regression analysis

This is an introductory statistics book designed to provide scientists with practical information needed to apply the most common statistical tests to laboratory research data. The book is designed to be practical and applicable, so only minimal information is devoted to theory or equations. Emphasis is placed on the underlying principles for effective data analysis and survey the statistical tests. It is of special value for scientists who have access to Minitab software. Examples are provides for all the statistical tests and explanation of the interpretation of these results presented with Minitab (similar to results for any common software package). The book is specifically designed to contribute to the AAPS series on advances in the pharmaceutical sciences. It benefits professional scientists or graduate students who have not had a formal statistics class, who had bad experiences in such classes, or who just fear/don't understand statistics. Chapter 1 focuses on terminology and essential elements of statistical testing. Statistics is often complicated by synonyms and this chapter established the terms used in the book and how rudiments interact to create statistical tests. Chapter 2 discussed descriptive statistics that are used to organize and summarize sample results. Chapter 3 discussed basic assumptions of probability, characteristics of a normal distribution, alternative approaches for non-normal distributions and introduces the topic of making inferences about a larger population based on a small sample from that population. Chapter 4 discussed hypothesis testing where computer output is interpreted and decisions are made regarding statistical significance. This chapter also deasl with the determination of appropriate sample sizes. The next three chapters focus on tests that make decisions about a population base on a small subset of information. Chapter 5 looks at statistical tests that evaluate where a significant difference exists. In Chapter 6 the tests try to determine the extent and importance of relationships. In contrast to fifth chapter, Chapter 7 presents tests that evaluate the equivalence, not the difference between levels being tested. The last chapter deals with potential outlier or aberrant values and how to statistically determine if they should be removed from the sample data. Each statistical test presented includes an example problem with the resultant software output and how to interpret the results. Minimal time is spent on the mathematical calculations or theory. For those interested in the associated equations, supplemental figures are presented for each test with respective formulas. In addition, Appendix D presents the equations and proof for every output result for the various examples. Examples and results from the appropriate statistical results are displayed using Minitab 18O. In addition to the results, the required steps to analyze data using Minitab are presented with the examples for those having access to this software. Numerous other software packages are available, including based data analysis with Excel.

This book presents an introduction to linear univariate and multivariate time series analysis, providing brief theoretical insights into each topic, and from the beginning illustrating the theory with software examples. As such, it quickly introduces readers to the peculiarities of each subject from both theoretical and the practical points of view. It also includes numerous examples and real-world applications that demonstrate how to handle different types of time series data. The associated software package, SSMMATLAB, is written in MATLAB and also runs on the free OCTAVE platform. The book focuses on linear time series models using a state space approach, with the Kalman filter and smoother as the main tools for model estimation, prediction and signal extraction. A chapter on state space models describes these tools and provides examples of their use with general state space models. Other topics discussed in the book include ARIMA; and transfer function and structural models; as well as signal extraction using the canonical decomposition in the univariate case, and VAR, VARMA, cointegrated VARMA, VARX, VARMAX, and multivariate structural models in the multivariate case. It also addresses spectral analysis, the use of fixed filters in a model-based approach, and automatic model identification procedures for ARIMA and transfer function models in the presence of outliers, interventions, complex seasonal patterns and other effects like Easter, trading day, etc. This book is intended for both students and researchers in various fields dealing with time series. The software provides numerous automatic procedures to handle common practical situations, but at the same time, readers with programming skills can write their own programs to deal with specific problems. Although the theoretical introduction to each topic is kept to a minimum, readers can consult the companion book 'Multivariate Time Series With Linear State Space Structure', by the same author, if they require more details.