Although power method polynomials based on the standard normal distributions have been used in many different contexts for the past 30 years, it was not until recently that the probability density function (pdf) and cumulative distribution function (cdf) were derived and made available. Focusing on both univariate and multivariate nonnormal data generation, Statistical Simulation: Power Method Polynomials and Other Transformations presents techniques for conducting a Monte Carlo simulation study. It shows how to use power method polynomials for simulating univariate and multivariate nonnormal distributions with specified cumulants and correlation matrices. The book first explores the methodology underlying the power method, before demonstrating this method through examples of standard normal, logistic, and uniform power method pdfs. It also discusses methods for improving the performance of a simulation based on power method polynomials. The book then develops simulation procedures for systems of linear statistical models, intraclass correlation coefficients, and correlated continuous variates and ranks. Numerical examples and results from Monte Carlo simulations illustrate these procedures. The final chapter describes how the g-and-h and generalized lambda distribution (GLD) transformations are special applications of the more general multivariate nonnormal data generation approach. Throughout the text, the author employs Mathematica (R) in a range of procedures and offers the source code for download online. Written by a longtime researcher of the power method, this book explains how to simulate nonnormal distributions via easy-to-use power method polynomials. By using the methodology and techniques developed in the text, readers can evaluate different transformations in terms of comparing percentiles, measures of central tendency, goodness-of-fit tests, and more.

Interest in predictive analytics of big data has grown exponentially in the four years since the publication of Statistical and Machine-Learning Data Mining: Techniques for Better Predictive Modeling and Analysis of Big Data, Second Edition. In the third edition of this bestseller, the author has completely revised, reorganized, and repositioned the original chapters and produced 13 new chapters of creative and useful machine-learning data mining techniques. In sum, the 43 chapters of simple yet insightful quantitative techniques make this book unique in the field of data mining literature. What is new in the Third Edition: The current chapters have been completely rewritten. The core content has been extended with strategies and methods for problems drawn from the top predictive analytics conference and statistical modeling workshops. Adds thirteen new chapters including coverage of data science and its rise, market share estimation, share of wallet modeling without survey data, latent market segmentation, statistical regression modeling that deals with incomplete data, decile analysis assessment in terms of the predictive power of the data, and a user-friendly version of text mining, not requiring an advanced background in natural language processing (NLP). Includes SAS subroutines which can be easily converted to other languages. As in the previous edition, this book offers detailed background, discussion, and illustration of specific methods for solving the most commonly experienced problems in predictive modeling and analysis of big data. The author addresses each methodology and assigns its application to a specific type of problem. To better ground readers, the book provides an in-depth discussion of the basic methodologies of predictive modeling and analysis. While this type of overview has been attempted before, this approach offers a truly nitty-gritty, step-by-step method that both tyros and experts in the field can enjoy playing with.

Offering deep insight into the connections between design choice and the resulting statistical analysis, Design of Experiments: An Introduction Based on Linear Models explores how experiments are designed using the language of linear statistical models. The book presents an organized framework for understanding the statistical aspects of experimental design as a whole within the structure provided by general linear models, rather than as a collection of seemingly unrelated solutions to unique problems. The core material can be found in the first thirteen chapters. These chapters cover a review of linear statistical models, completely randomized designs, randomized complete blocks designs, Latin squares, analysis of data from orthogonally blocked designs, balanced incomplete block designs, random block effects, split-plot designs, and two-level factorial experiments. The remainder of the text discusses factorial group screening experiments, regression model design, and an introduction to optimal design. To emphasize the practical value of design, most chapters contain a short example of a real-world experiment. Details of the calculations performed using R, along with an overview of the R commands, are provided in an appendix. This text enables students to fully appreciate the fundamental concepts and techniques of experimental design as well as the real-world value of design. It gives them a profound understanding of how design selection affects the information obtained in an experiment.

People tend to rank values of all kinds linearly from good to bad, but there is little reason to think that this is reasonable or correct. This book argues, to the contrary, that values are often partially ordered and hence frequently incomparable. Proceeding logically from a small set of axioms, John Nolt examines the great variety of partially ordered value structures, exposing fallacies that arise from overlooking them. He reveals various ways in which incomparability is obscured: using linear indices to summarize partially ordered data, relying on an inadequately defined concept of parity, or conflating incomparability with vagueness. Incomparability can enrich and clarify a range of topics including the paradoxes of Derek Parfit, rational decision theory, and the infinite values of theology. Finally, Nolt shows how to generalize many of the concepts introduced earlier, explores the intricate depths of certain noteworthy partially ordered value structures, and argues for the finitude of value. Incomparable Values will be of interest to scholars and advanced students working in ethics, value theory, rational decision theory, and logic.

Optimality Conditions in Convex Optimization explores an important and central issue in the field of convex optimization: optimality conditions. It brings together the most important and recent results in this area that have been scattered in the literature-notably in the area of convex analysis-essential in developing many of the important results in this book, and not usually found in conventional texts. Unlike other books on convex optimization, which usually discuss algorithms along with some basic theory, the sole focus of this book is on fundamental and advanced convex optimization theory. Although many results presented in the book can also be proved in infinite dimensions, the authors focus on finite dimensions to allow for much deeper results and a better understanding of the structures involved in a convex optimization problem. They address semi-infinite optimization problems; approximate solution concepts of convex optimization problems; and some classes of non-convex problems which can be studied using the tools of convex analysis. They include examples wherever needed, provide details of major results, and discuss proofs of the main results.

Taking into account the standards of the Basel Accord, Operational Risk Modelling and Management presents a simulation model for generating the loss distribution of operational risk. It also examines a multitude of management issues that must be considered when adjusting the quantitative results of a comprehensive model. The book emphasizes techniques that can be understood and applied by practitioners. In the quantitative portions of the text, the author supplies key concepts and definitions without stating theorems or delving into mathematical proofs. He also offers references for readers looking for further background information. In addition, the book includes a Monte Carlo simulation of risk capital in the form of a run-through example of risk calculations based on data from a quantitative impact study. Since the computations are too complicated for a scripting language, a prototypical software program can be downloaded from www.garrulus.com Helping you navigate the tricky world of risk calculation and management, this book presents two main building blocks for determining how much capital needs to be reserved for operational risk. It employs the loss distribution approach as a model for calculating the risk capital figure and explains risk mitigation through management and management's actuations.

Based on the many approaches available for dealing with large-scale systems (LSS), Decentralized Control and Filtering in Interconnected Dynamical Systems supplies a rigorous framework for studying the analysis, stability, and control problems of LSS. Providing an overall assessment of LSS theories, it addresses model order reduction, parametric uncertainties, time delays, and control estimator gain perturbations. Taking readers on a guided tour through LSS, the book examines recent trends and approaches and reviews past methods and results from a contemporary perspective. It traces the progress of research along three eras: Fundamental era in which the basic conceptual frameworks, major ideas, and operational methodologies are laid down Contemporary era in which several of the workable methods and techniques are established and applied to many application areas Advanced era in which different high-level schemes and configurations are being developed to meet accelerated technological advancements Focusing on robust, reliable, and/or resilient decentralized design methods based on linear matrix inequalities framework, the author offers suggestions for improvements to current approaches. He addresses the dominating sources of difficulties due to dimensionality, information structure constraints, uncertainties, and time delays. Drawing attention to key issues, the text is supported by proofs, efficient computational methods, end-of-chapter problems, and approximately 1,300 equations.

We live in a world that is not quite "right." The central tenet of statistical inquiry is that Observation = Truth + Error because even the most careful of scientific investigations have always been bedeviled by uncertainty. Our attempts to measure things are plagued with small errors. Our attempts to understand our world are blocked by blunders. And, unfortunately, in some cases, people have been known to lie. In this long-awaited follow-up to his well-regarded bestseller, The Lady Tasting Tea, David Salsburg opens a door to the amazing widespread use of statistical methods by looking at historical examples of errors, blunders and lies from areas as diverse as archeology, law, economics, medicine, psychology, sociology, Biblical studies, history, and war-time espionage. In doing so, he shows how, upon closer statistical investigation, errors and blunders often lead to useful information. And how statistical methods have been used to uncover falsified data. Beginning with Edmund Halley's examination of the Transit of Venus and ending with a discussion of how many tanks Rommel had during the Second World War, the author invites the reader to come along on this easily accessible and fascinating journey of how to identify the nature of errors, minimize the effects of blunders, and figure out who the liars are.

Unlike much of the existing literature, Stochastic Finance: A Numeraire Approach treats price as a number of units of one asset needed for an acquisition of a unit of another asset instead of expressing prices in dollar terms exclusively. This numeraire approach leads to simpler pricing options for complex products, such as barrier, lookback, quanto, and Asian options. Most of the ideas presented rely on intuition and basic principles, rather than technical computations. The first chapter of the book introduces basic concepts of finance, including price, no arbitrage, portfolio, financial contracts, the First Fundamental Theorem of Asset Pricing, and the change of numeraire formula. Subsequent chapters apply these general principles to three kinds of models: binomial, diffusion, and jump models. The author uses the binomial model to illustrate the relativity of the reference asset. In continuous time, he covers both diffusion and jump models in the evolution of price processes. The book also describes term structure models and numerous options, including European, barrier, lookback, quanto, American, and Asian. Classroom-tested at Columbia University to graduate students, Wall Street professionals, and aspiring quants, this text provides a deep understanding of derivative contracts. It will help a variety of readers from the dynamic world of finance, from practitioners who want to expand their knowledge of stochastic finance, to students who want to succeed as professionals in the field, to academics who want to explore relatively advanced techniques of the numeraire change.

Handbook of Empirical Economics and Finance explores the latest developments in the analysis and modeling of economic and financial data. Well-recognized econometric experts discuss the rapidly growing research in economics and finance and offer insight on the future direction of these fields. Focusing on micro models, the first group of chapters describes the statistical issues involved in the analysis of econometric models with cross-sectional data often arising in microeconomics. The book then illustrates time series models that are extensively used in empirical macroeconomics and finance. The last set of chapters explores the types of panel data and spatial models that are becoming increasingly significant in analyzing complex economic behavior and policy evaluations. This handbook brings together both background material and new methodological and applied results that are extremely important to the current and future frontiers in empirical economics and finance. It emphasizes inferential issues that transpire in the analysis of cross-sectional, time series, and panel data-based empirical models in economics, finance, and related disciplines.

In their bestselling MATHEMATICAL STATISTICS WITH APPLICATIONS, premiere authors Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors' use of practical applications and excellent exercises helps you discover the nature of statistics and understand its essential role in scientific research.

For surveys involving sensitive questions, randomized response techniques (RRTs) and other indirect questions are helpful in obtaining survey responses while maintaining the privacy of the respondents. Written by one of the leading experts in the world on RR, Randomized Response and Indirect Questioning Techniques in Surveys describes the current state of RR as well as emerging developments in the field. The author also explains how to extend RR to situations employing unequal probability sampling. While the theory of RR has grown phenomenally, the area has not kept pace in practice. Covering both theory and practice, the book first discusses replacing a direct response (DR) with an RR in a simple random sample with replacement (SRSWR). It then emphasizes how the application of RRTs in the estimation of attribute or quantitative features is valid for selecting respondents in a general manner. The author examines different ways to treat maximum likelihood estimation; covers optional RR devices, which provide alternatives to compulsory randomized response theory; and presents RR techniques that encompass quantitative variables, including those related to stigmatizing characteristics. He also gives his viewpoint on alternative RR techniques, including the item count technique, nominative technique, and three-card method.

Explores the Origin of the Recent Banking Crisis and how to Preclude Future Crises Shedding new light on the recent worldwide banking debacle, The Banking Crisis Handbook presents possible remedies as to what should have been done prior, during, and after the crisis. With contributions from well-known academics and professionals, the book contains exclusive, new research that will undoubtedly assist bank executives, risk management departments, and other financial professionals to attain a clear picture of the banking crisis and prevent future banking collapses. The first part of the book explains how the crisis originated. It discusses the role of subprime mortgages, shadow banks, ineffective risk management, poor financial regulations, and hedge funds in causing the collapse of financial systems. The second section examines how the crisis affected the global market as well as individual countries and regions, such as Asia and Greece. In the final part, the book explores short- and long-term solutions, including government intervention, financial regulations, efficient bank default risk approaches, and methods to evaluate credit risk. It also looks at when government intervention in financial markets can be ethically justified.

THE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITY Written in a clear, accessible, and comprehensive manner, the Handbook of Probability presents the fundamentals of probability with an emphasis on the balance of theory, application, and methodology. Utilizing basic examples throughout, the handbook expertly transitions between concepts and practice to allow readers an inclusive introduction to the field of probability. The book provides a useful format with self-contained chapters, allowing the reader easy and quick reference. Each chapter includes an introduction, historical background, theory and applications, algorithms, and exercises. The Handbook of Probability offers coverage of: * Probability Space * Probability Measure * Random Variables * Random Vectors in Rn * Characteristic Function * Moment Generating Function * Gaussian Random Vectors * Convergence Types * Limit Theorems The Handbook of Probability is an ideal resource for researchers and practitioners in numerous fields, such as mathematics, statistics, operations research, engineering, medicine, and finance, as well as a useful text for graduate students.

This important three volume set is a collection of Edgeworth's published writings in the areas of statistics and probability. There is a newly-emerging interest in probability theory as a basis for economic thought and this collection makes the writings of Edgeworth more accessible.A new introduction written by the editor covers the biographical details, a brief abstract of each of the articles and the basis of their selection is also included.

Written with students and professors in mind, Analysis of Queues: Methods and Applications combines coverage of classical queueing theory with recent advances in studying stochastic networks. Exploring a broad range of applications, the book contains plenty of solved problems, exercises, case studies, paradoxes, and numerical examples. In addition to the standard single-station and single class discrete queues, the book discusses models for multi-class queues and queueing networks as well as methods based on fluid scaling, stochastic fluid flows, continuous parameter Markov processes, and quasi-birth-and-death processes, to name a few. It describes a variety of applications including computer-communication networks, information systems, production operations, transportation, and service systems such as healthcare, call centers and restaurants.

Covers statistical concepts, methods and applications related to all aspects of survival analysis with cure, integration of insights gained from statistical analysis to decision-marking and inference in cancer research Self-contained as sufficient the technical details and statistical background are provided to make its materials easy to grasp Timely book on most relevant and important issues on cure models by experienced statistical researchers Includes Applications to real-life problems Inclusion of R codes for some of the novel methods and high-impact studies

Review of the First Edition: The authors strive to reduce theory to a minimum, which makes it a self-learning text that is comprehensible for biologists, physicians, etc. who lack an advanced mathematics background. Unlike in many other textbooks, R is not introduced with meaningless toy examples; instead the reader is taken by the hand and shown around some analyses, graphics, and simulations directly relating to meta-analysis... A useful hands-on guide for practitioners who want to familiarize themselves with the fundamentals of meta-analysis and get started without having to plough through theorems and proofs. -Journal of Applied Statistics Statistical Meta-Analysis with R and Stata, Second Edition provides a thorough presentation of statistical meta-analyses (MA) with step-by-step implementations using R/Stata. The authors develop analysis step by step using appropriate R/Stata functions, which enables readers to gain an understanding of meta-analysis methods and R/Stata implementation so that they can use these two popular software packages to analyze their own meta-data. Each chapter gives examples of real studies compiled from the literature. After presenting the data and necessary background for understanding the applications, various methods for analyzing meta-data are introduced. The authors then develop analysis code using the appropriate R/Stata packages and functions. What's New in the Second Edition: Adds Stata programs along with the R programs for meta-analysis Updates all the statistical meta-analyses with R/Stata programs Covers fixed-effects and random-effects MA, meta-regression, MA with rare-event, and MA-IPD vs MA-SS Adds five new chapters on multivariate MA, publication bias, missing data in MA, MA in evaluating diagnostic accuracy, and network MA Suitable as a graduate-level text for a meta-data analysis course, the book is also a valuable reference for practitioners and biostatisticians (even those with little or no experience in using R or Stata) in public health, medical research, governmental agencies, and the pharmaceutical industry.

Latent Variable Models: An Introduction to Factor, Path, and Structural Equation Analysis introduces latent variable models by utilizing path diagrams to explain the relationships in the models. This approach helps less mathematically-inclined readers to grasp the underlying relations among path analysis, factor analysis, and structural equation modeling, and to set up and carry out such analyses. This revised and expanded fifth edition again contains key chapters on path analysis, structural equation models, and exploratory factor analysis. In addition, it contains new material on composite reliability, models with categorical data, the minimum average partial procedure, bi-factor models, and communicating about latent variable models. The informal writing style and the numerous illustrative examples make the book accessible to readers of varying backgrounds. Notes at the end of each chapter expand the discussion and provide additional technical detail and references. Moreover, most chapters contain an extended example in which the authors work through one of the chapter's examples in detail to aid readers in conducting similar analyses with their own data. The book and accompanying website provide all of the data for the book's examples as well as syntax from latent variable programs so readers can replicate the analyses. The book can be used with any of a variety of computer programs, but special attention is paid to LISREL and R. An important resource for advanced students and researchers in numerous disciplines in the behavioral sciences, education, business, and health sciences, Latent Variable Models is a practical and readable reference for those seeking to understand or conduct an analysis using latent variables.

Reliably optimizing a new treatment in humans is a critical first step in clinical evaluation since choosing a suboptimal dose or schedule may lead to failure in later trials. At the same time, if promising preclinical results do not translate into a real treatment advance, it is important to determine this quickly and terminate the clinical evaluation process to avoid wasting resources. Bayesian Designs for Phase I-II Clinical Trials describes how phase I-II designs can serve as a bridge or protective barrier between preclinical studies and large confirmatory clinical trials. It illustrates many of the severe drawbacks with conventional methods used for early-phase clinical trials and presents numerous Bayesian designs for human clinical trials of new experimental treatment regimes. Written by research leaders from the University of Texas MD Anderson Cancer Center, this book shows how Bayesian designs for early-phase clinical trials can explore, refine, and optimize new experimental treatments. It emphasizes the importance of basing decisions on both efficacy and toxicity.

This short book introduces the main ideas of statistical inference in a way that is both user friendly and mathematically sound. Particular emphasis is placed on the common foundation of many models used in practice. In addition, the book focuses on the formulation of appropriate statistical models to study problems in business, economics, and the social sciences, as well as on how to interpret the results from statistical analyses. The book will be useful to students who are interested in rigorous applications of statistics to problems in business, economics and the social sciences, as well as students who have studied statistics in the past, but need a more solid grounding in statistical techniques to further their careers. Jacco Thijssen is professor of finance at the University of York, UK. He holds a PhD in mathematical economics from Tilburg University, Netherlands. His main research interests are in applications of optimal stopping theory, stochastic calculus, and game theory to problems in economics and finance. Professor Thijssen has earned several awards for his statistics teaching.

Introduction to Statistics with SPSS offers an introduction to statistics that can be used before, during or after a course on statistics. Covering a wide range of terms and techniques, including simple and multiple regressions, this book guides the student to enter data from a simple research project into a computer, provide an adequate analysis of the data and present a report on the findings.

Multi-State Survival Models for Interval-Censored Data introduces methods to describe stochastic processes that consist of transitions between states over time. It is targeted at researchers in medical statistics, epidemiology, demography, and social statistics. One of the applications in the book is a three-state process for dementia and survival in the older population. This process is described by an illness-death model with a dementia-free state, a dementia state, and a dead state. Statistical modelling of a multi-state process can investigate potential associations between the risk of moving to the next state and variables such as age, gender, or education. A model can also be used to predict the multi-state process. The methods are for longitudinal data subject to interval censoring. Depending on the definition of a state, it is possible that the time of the transition into a state is not observed exactly. However, when longitudinal data are available the transition time may be known to lie in the time interval defined by two successive observations. Such an interval-censored observation scheme can be taken into account in the statistical inference. Multi-state modelling is an elegant combination of statistical inference and the theory of stochastic processes. Multi-State Survival Models for Interval-Censored Data shows that the statistical modelling is versatile and allows for a wide range of applications.

The purpose of this book is to introduce novice researchers to the tools of meta-analysis and meta-regression analysis and to summarize the state of the art for existing practitioners. Meta-regression analysis addresses the rising "Tower of Babel" that current economics and business research has become. Meta-analysis is the statistical analysis of previously published, or reported, research findings on a given hypothesis, empirical effect, phenomenon, or policy intervention. It is a systematic review of all the relevant scientific knowledge on a specific subject and is an essential part of the evidence-based practice movement in medicine, education and the social sciences. However, research in economics and business is often fundamentally different from what is found in the sciences and thereby requires different methods for its synthesis-meta-regression analysis. This book develops, summarizes, and applies these meta-analytic methods.

This edited volume focuses on the latest developments in classification and data science and covers a wide range of topics in the context of data analysis and related areas, e.g. the analysis of complex data, analysis of qualitative data, methods for high-dimensional data, dimensionality reduction, data visualization, multivariate statistical methods, and various applications to real data in the social sciences, medical sciences, and other disciplines. In addition to sharing theoretical and methodological findings, the book shows how to apply the proposed methods to a variety of problems - e.g. in consumer behavior, decision-making, marketing data and social network structures. Both methodological aspects and applications to a wide range of areas such as economics, behavioral science, marketing science, management science and the social sciences are covered. The book is chiefly intended for researchers and practitioners who are interested in the latest developments and practical applications in these fields, as well as applied statisticians and data analysts. Its combination of methodological advances with a wide range of real-world applications gathered from several fields makes it of unique value in helping readers solve their research problems.