The Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response.

The theoretical properties and applications are also reviewed in detail for other related distributions, such as the inverted Dirichlet distribution, Dirichlet-multinomial distribution, the truncated Dirichlet distribution, the generalized Dirichlet distribution, Hyper-Dirichlet distribution, scaled Dirichlet distribution, mixed Dirichlet distribution, Liouville distribution, and the generalized Liouville distribution.

Key Features: Presents many of the results and applications that are scattered throughout the literature in one single volume.
Looks at the most recent results such as survival function and characteristic function for the uniform distributions over the hyper-plane and simplex; distribution for linear function of Dirichlet components; estimation via the expectation-maximization gradient algorithm and application; etc.
Likelihood and Bayesian analyses of incomplete categorical data by using GDD, NDD, and the generalized Dirichlet distribution are illustrated in detail through the EM algorithm and data augmentation structure.Presents a systematic exposition of the Dirichlet-multinomial distribution for multinomial data with extra variation which cannot be handled by the multinomial distribution.
S-plus/R codes are featured along with practical examples illustrating the methods.

Practitioners and researchers working in areas such as medical science, biological science and social science will benefit from this book.

This book is about learning from data using the Generalized Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS extends the Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) to accommodate large complex datasets, which are increasingly prevalent. In particular, the GAMLSS statistical framework enables flexible regression and smoothing models to be fitted to the data. The GAMLSS model assumes that the response variable has any parametric (continuous, discrete or mixed) distribution which might be heavy- or light-tailed, and positively or negatively skewed. In addition, all the parameters of the distribution (location, scale, shape) can be modelled as linear or smooth functions of explanatory variables. Key Features: Provides a broad overview of flexible regression and smoothing techniques to learn from data whilst also focusing on the practical application of methodology using GAMLSS software in R. Includes a comprehensive collection of real data examples, which reflect the range of problems addressed by GAMLSS models and provide a practical illustration of the process of using flexible GAMLSS models for statistical learning. R code integrated into the text for ease of understanding and replication. Supplemented by a website with code, data and extra materials. This book aims to help readers understand how to learn from data encountered in many fields. It will be useful for practitioners and researchers who wish to understand and use the GAMLSS models to learn from data and also for students who wish to learn GAMLSS through practical examples.

Developed from the author's course at the Ecole Polytechnique, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic processes in continuous time and their link with partial differential equations (PDEs). It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method. The book begins with a history of Monte-Carlo methods and an overview of three typical Monte-Carlo problems: numerical integration and computation of expectation, simulation of complex distributions, and stochastic optimization. The remainder of the text is organized in three parts of progressive difficulty. The first part presents basic tools for stochastic simulation and analysis of algorithm convergence. The second part describes Monte-Carlo methods for the simulation of stochastic differential equations. The final part discusses the simulation of non-linear dynamics.

AI framework intended to solve a problem of bias-variance tradeoff for supervised learning methods in real-life applications. The AI framework comprises of bootstrapping to create multiple training and testing data sets with various characteristics, design and analysis of statistical experiments to identify optimal feature subsets and optimal hyper-parameters for ML methods, data contamination to test for the robustness of the classifiers. Key Features: Using ML methods by itself doesn't ensure building classifiers that generalize well for new data Identifying optimal feature subsets and hyper-parameters of ML methods can be resolved using design and analysis of statistical experiments Using a bootstrapping approach to massive sampling of training and tests datasets with various data characteristics (e.g.: contaminated training sets) allows dealing with bias Developing of SAS-based table-driven environment allows managing all meta-data related to the proposed AI framework and creating interoperability with R libraries to accomplish variety of statistical and machine-learning tasks Computer programs in R and SAS that create AI framework are available on GitHub

An Introduction to Nonparametric Statistics presents techniques for statistical analysis in the absence of strong assumptions about the distributions generating the data. Rank-based and resampling techniques are heavily represented, but robust techniques are considered as well. These techniques include one-sample testing and estimation, multi-sample testing and estimation, and regression. Attention is paid to the intellectual development of the field, with a thorough review of bibliographical references. Computational tools, in R and SAS, are developed and illustrated via examples. Exercises designed to reinforce examples are included. Features Rank-based techniques including sign, Kruskal-Wallis, Friedman, Mann-Whitney and Wilcoxon tests are presented Tests are inverted to produce estimates and confidence intervals Multivariate tests are explored Techniques reflecting the dependence of a response variable on explanatory variables are presented Density estimation is explored The bootstrap and jackknife are discussed This text is intended for a graduate student in applied statistics. The course is best taken after an introductory course in statistical methodology, elementary probability, and regression. Mathematical prerequisites include calculus through multivariate differentiation and integration, and, ideally, a course in matrix algebra.

- the book can be used by beginners in the field, tracking from basic principles to how to bend the rules, in reader-friendly language throughout - the book is based on a popular blog which dovetails as a fantastic companion website: https://questionsindataviz.com/ - the author is a very experienced and well-respected practitioner in the field, with a good-size following on social media: https://twitter.com/theneilrichards

-Up-to-date with cutting edge topics -Suitable for professional quants and as library reference for students of finance and financial mathematics

Factor Analysis and Dimension Reduction in R provides coverage, with worked examples, of a large number of dimension reduction procedures along with model performance metrics to compare them. Factor analysis in the form of principal components analysis (PCA) or principal factor analysis (PFA) is familiar to most social scientists. However, what is less familiar is understanding that factor analysis is a subset of the more general statistical family of dimension reduction methods. The social scientist's toolkit for factor analysis problems can be expanded to include the range of solutions this book presents. In addition to covering FA and PCA with orthogonal and oblique rotation, this book's coverage includes higher-order factor models, bifactor models, models based on binary and ordinal data, models based on mixed data, generalized low-rank models, cluster analysis with GLRM, models involving supplemental variables or observations, Bayesian factor analysis, regularized factor analysis, testing for unidimensionality, and prediction with factor scores. The second half of the book deals with other procedures for dimension reduction. These include coverage of kernel PCA, factor analysis with multidimensional scaling, locally linear embedding models, Laplacian eigenmaps, diffusion maps, force directed methods, t-distributed stochastic neighbor embedding, independent component analysis (ICA), dimensionality reduction via regression (DRR), non-negative matrix factorization (NNMF), Isomap, Autoencoder, uniform manifold approximation and projection (UMAP) models, neural network models, and longitudinal factor analysis models. In addition, a special chapter covers metrics for comparing model performance. Features of this book include: Numerous worked examples with replicable R code Explicit comprehensive coverage of data assumptions Adaptation of factor methods to binary, ordinal, and categorical data Residual and outlier analysis Visualization of factor results Final chapters that treat integration of factor analysis with neural network and time series methods Presented in color with R code and introduction to R and RStudio, this book will be suitable for graduate-level and optional module courses for social scientists, and on quantitative methods and multivariate statistics courses.

This book is written for the love of numbers. It tells their story, shows how they were invented and used to quantify our world, and explains what quantitative data mean for our lives. It aspires to contribute to overall numeracy through a tour de force presentation of the production, use, and evolution of data. Understanding our physical world, our economies, and our societies through quantification has been a persistent feature of human evolution. This book starts with a narrative on why and how our ancestors were driven to the invention of number, which is then traced to the eventual arrival at our number system. This is followed by a discussion of how numbers were used for counting, how they enabled the measurement of physical quantities, and how they led to the estimation of man-made and abstract notions in the socio-economic domain. As data don't fall like manna from the sky, a unique feature of this book is that it explains from a teacher's perspective how they're really conceived in our minds, how they're actually produced from individual observations, and how this defines their meaning and interpretation. It discusses the significance of standards, the use of taxonomies, and clarifies a series of misconceptions regarding the making of data. The book then describes the switch to a new research paradigm and its implications, highlights the arrival of microdata, illustrates analytical uses of data, and closes with a look at the future of data and our own role in it.

In-depth coverage of discrete-time theory and methodology. Numerous, fully worked out examples and exercises in every chapter. Mathematically rigorous and consistent yet bridging various basic and more advanced concepts. Judicious balance of financial theory, mathematical, and computational methods. Guide to Material.

The subject of this book is applied Bayesian methods for chemistry, manufacturing, and control (CMC) studies in the biopharmaceutical industry. The book has multiple authors from industry and academia, each contributing a case study (chapter). The collection of case studies covers a broad array of CMC topics, including stability analysis, analytical method development, specification setting, process development and optimization, process control, experimental design, dissolution testing, and comparability studies. The analysis of each case study includes a presentation of code and reproducible output. This book is written with an academic level aimed at practicing nonclinical biostatisticians, most of whom have graduate degrees in statistics. * First book of its kind focusing strictly on CMC Bayesian case studies * Case studies with code and output * Representation from several companies across the industry as well as academia * Authors are leading and well-known Bayesian statisticians in the CMC field * Accompanying website with code for reproducibility * Reflective of real-life industry applications/problems

This book develops new techniques in formal epistemology and applies them to the challenge of Cartesian skepticism. It introduces two formats of epistemic evaluation that should be of interest to epistemologists and philosophers of science: the dual-component format, which evaluates a statement on the basis of its safety and informativeness, and the relative-divergence format, which evaluates a probabilistic model on the basis of its complexity and goodness of fit with data. Tomoji Shogenji shows that the former lends support to Cartesian skepticism, but the latter allows us to defeat Cartesian skepticism. Along the way, Shogenji addresses a number of related issues in epistemology and philosophy of science, including epistemic circularity, epistemic closure, and inductive skepticism.

Quantitative Methods in Transportation provides the most useful, simple, and advanced quantitative techniques for solving real-life transportation engineering problems. It aims to help transportation engineers and analysts to predict travel and freight demand, plan new transportation networks, and develop various traffic control strategies that are safer, more cost effective, and greener. Transportation networks can be exceptionally large, and this makes many transportation problems combinatorial, and the challenges are compounded by the stochastic and independent nature of trip-planners decision making. Methods outlined in this book range from linear programming, multi-attribute decision making, data envelopment analysis, probability theory, and simulation to computer techniques such as genetic algorithms, simulated annealing, tabu search, ant colony optimization, and bee colony optimization. The book is supported with problems and has a solutions manual to aid course instructors.

Praise for the first edition: Principles of Uncertainty is a profound and mesmerising book on the foundations and principles of subjectivist or behaviouristic Bayesian analysis. ... the book is a pleasure to read. And highly recommended for teaching as it can be used at many different levels. ... A must-read for sure!-Christian Robert, CHANCEIt's a lovely book, one that I hope will be widely adopted as a course textbook. -Michael Jordan, University of California, Berkeley, USA Like the prize-winning first edition, Principles of Uncertainty, Second Edition is an accessible, comprehensive text on the theory of Bayesian Statistics written in an appealing, inviting style, and packed with interesting examples. It presents an introduction to the subjective Bayesian approach which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. This new edition has been updated throughout and features new material on Nonparametric Bayesian Methods, the Dirichlet distribution, a simple proof of the central limit theorem, and new problems. Key Features: First edition won the 2011 DeGroot Prize Well-written introduction to theory of Bayesian statistics Each of the introductory chapters begins by introducing one new concept or assumption Uses "just-in-time mathematics"-the introduction to mathematical ideas just before they are applied

Urban Informatics: Using Big Data to Understand and Serve Communities introduces the reader to the tools of data management, analysis, and manipulation using R statistical software. Designed for undergraduate and above level courses, this book is an ideal onramp for the study of urban informatics and how to translate novel data sets into new insights and practical tools. The book follows a unique pedagogical approach developed by the author to enable students to build skills by pursuing projects that inspire and motivate them. Each chapter has an Exploratory Data Assignment that prompts readers to practice their new skills on a data set of their choice. These assignments guide readers through the process of becoming familiar with the contents of a novel data set and communicating meaningful insights from the data to others. Key Features: The technical curriculum consists of both data management and analytics, including both as needed to become acquainted with and reveal the content of a new data set. Content that is contextualized in real-world applications relevant to community concerns. Unit-level assignments that educators might use as midterms or otherwise. These include Community Experience assignments that prompt students to evaluate the assumptions they have made about their data against real world information. All data sets are publicly available through the Boston Data Portal.

Multi-Criteria Decision-Making (MCDM) includes methods and tools for modeling and solving complex problems. MCDM has become popular in the production and service sectors to improve the quality of service, reduce costs, and make people more prosperous. This book illustrates applications through case studies focused on disaster management. With a presentation of both Multi-Attribute Decision-Making (MADM) and Multi-Objective Decision-Making (MODM) models, this is the first book to merge these methods and tools with disaster management. This book raises awareness for society and decision-makers on how to measure readiness and what necessary preventive measures need to be taken. It offers models and case studies that can be easily adapted to solve complex problems and find solutions in other fields. Multi-Criteria Decision Analysis: Case Studies in Disaster Management will offer new insights to researchers working in the areas of industrial engineering, systems engineering, healthcare systems, operations research, mathematics, business, computer science, and disaster management, and, hopefully, the book will also stimulate further work in MCDM.

Computational finance is increasingly important in the financial industry, as a necessary instrument for applying theoretical models to real-world challenges. Indeed, many models used in practice involve complex mathematical problems, for which an exact or a closed-form solution is not available. Consequently, we need to rely on computational techniques and specific numerical algorithms. This book combines theoretical concepts with practical implementation. Furthermore, the numerical solution of models is exploited, both to enhance the understanding of some mathematical and statistical notions, and to acquire sound programming skills in MATLAB (R), which is useful for several other programming languages also. The material assumes the reader has a relatively limited knowledge of mathematics, probability, and statistics. Hence, the book contains a short description of the fundamental tools needed to address the two main fields of quantitative finance: portfolio selection and derivatives pricing. Both fields are developed here, with a particular emphasis on portfolio selection, where the author includes an overview of recent approaches. The book gradually takes the reader from a basic to medium level of expertise by using examples and exercises to simplify the understanding of complex models in finance, giving them the ability to place financial models in a computational setting. The book is ideal for courses focusing on quantitative finance, asset management, mathematical methods for economics and finance, investment banking, and corporate finance.

Praise for the first edition: [This book] reflects the extensive experience and significant contributions of the author to non-linear and non-Gaussian modeling. ... [It] is a valuable book, especially with its broad and accessible introduction of models in the state-space framework. -Statistics in Medicine What distinguishes this book from comparable introductory texts is the use of state-space modeling. Along with this come a number of valuable tools for recursive filtering and smoothing, including the Kalman filter, as well as non-Gaussian and sequential Monte Carlo filters. -MAA Reviews Introduction to Time Series Modeling with Applications in R, Second Edition covers numerous stationary and nonstationary time series models and tools for estimating and utilizing them. The goal of this book is to enable readers to build their own models to understand, predict and master time series. The second edition makes it possible for readers to reproduce examples in this book by using the freely available R package TSSS to perform computations for their own real-world time series problems. This book employs the state-space model as a generic tool for time series modeling and presents the Kalman filter, the non-Gaussian filter and the particle filter as convenient tools for recursive estimation for state-space models. Further, it also takes a unified approach based on the entropy maximization principle and employs various methods of parameter estimation and model selection, including the least squares method, the maximum likelihood method, recursive estimation for state-space models and model selection by AIC. Along with the standard stationary time series models, such as the AR and ARMA models, the book also introduces nonstationary time series models such as the locally stationary AR model, the trend model, the seasonal adjustment model, the time-varying coefficient AR model and nonlinear non-Gaussian state-space models. About the Author: Genshiro Kitagawa is a project professor at the University of Tokyo, the former Director-General of the Institute of Statistical Mathematics, and the former President of the Research Organization of Information and Systems.

Epidemic trend analysis, timeline progression, prediction, and recommendation are critical for initiating effective public health control strategies, and AI and data analytics play an important role in epidemiology, diagnostic, and clinical fronts. The focus of this book is data analytics for COVID-19, which includes an overview of COVID-19 in terms of epidemic/pandemic, data processing and knowledge extraction. Data sources, storage and platforms are discussed along with discussions on data models, their performance, different big data techniques, tools and technologies. This book also addresses the challenges in applying analytics to pandemic scenarios, case studies and control strategies. Aimed at Data Analysts, Epidemiologists and associated researchers, this book: discusses challenges of AI model for big data analytics in pandemic scenarios; explains how different big data analytics techniques can be implemented; provides a set of recommendations to minimize infection rate of COVID-19; summarizes various techniques of data processing and knowledge extraction; enables users to understand big data analytics techniques required for prediction purposes.

Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.

Repeated measures data arise when the same characteristic is measured on each case or subject at several times or under several conditions. There is a multitude of techniques available for analysing such data and in the past this has led to some confusion. This book describes the whole spectrum of approaches, beginning with very simple and crude methods, working through intermediate techniques commonly used by consultant statisticians, and concluding with more recent and advanced methods. Those covered include multiple testing, response feature analysis, univariate analysis of variance approaches, multivariate analysis of variance approaches, regression models, two-stage line models, approaches to categorical data and techniques for analysing crossover designs. The theory is illustrated with examples, using real data brought to the authors during their work as statistical consultants.

This book discusses Change Management Impact Analysis and how this method is used to analysis the risks and benefits of a change management initiative when it pertains to obtaining critical insight into how the change management program budget should be allotted. The process also offers useful indicators for what areas within the system should be monitored during the change management process. This book presents theoretical analysis of practical implications and surveys, along with analysis. It covers the functions aimed at identifying various stakeholders associated with the software such as requirement component, design component, and class component. The book talks about the interrelationship between the change and the effects on the rest of the system and dives deeper to include the critical role that the analysis places on the existing multiple functions such as estimating the development costs, the project overhead costs, cost for the modification of the system, and system strength or detecting errors in the system during the process. Case studies are also included to help researchers and practitioners to absorb the material presented. This book is useful to graduate students, researchers, academicians, institutions, and professionals that interested in exploring the areas of Impact Analysis.

Modern computer-intensive statistical methods play a key role in solving many problems across a wide range of scientific disciplines. Like its bestselling predecessors, the fourth edition of Randomization, Bootstrap and Monte Carlo Methods in Biology illustrates a large number of statistical methods with an emphasis on biological applications. The focus is now on the use of randomization, bootstrapping, and Monte Carlo methods in constructing confidence intervals and doing tests of significance. The text provides comprehensive coverage of computer-intensive applications, with data sets available online. Features Presents an overview of computer-intensive statistical methods and applications in biology Covers a wide range of methods including bootstrap, Monte Carlo, ANOVA, regression, and Bayesian methods Makes it easy for biologists, researchers, and students to understand the methods used Provides information about computer programs and packages to implement calculations, particularly using R code Includes a large number of real examples from a range of biological disciplines Written in an accessible style, with minimal coverage of theoretical details, this book provides an excellent introduction to computer-intensive statistical methods for biological researchers. It can be used as a course text for graduate students, as well as a reference for researchers from a range of disciplines. The detailed, worked examples of real applications will enable practitioners to apply the methods to their own biological data.

Nonparametric Models for Longitudinal Data with Implementations in R presents a comprehensive summary of major advances in nonparametric models and smoothing methods with longitudinal data. It covers methods, theories, and applications that are particularly useful for biomedical studies in the era of big data and precision medicine. It also provides flexible tools to describe the temporal trends, covariate effects and correlation structures of repeated measurements in longitudinal data. This book is intended for graduate students in statistics, data scientists and statisticians in biomedical sciences and public health. As experts in this area, the authors present extensive materials that are balanced between theoretical and practical topics. The statistical applications in real-life examples lead into meaningful interpretations and inferences. Features: Provides an overview of parametric and semiparametric methods Shows smoothing methods for unstructured nonparametric models Covers structured nonparametric models with time-varying coefficients Discusses nonparametric shared-parameter and mixed-effects models Presents nonparametric models for conditional distributions and functionals Illustrates implementations using R software packages Includes datasets and code in the authors' website Contains asymptotic results and theoretical derivations Both authors are mathematical statisticians at the National Institutes of Health (NIH) and have published extensively in statistical and biomedical journals. Colin O. Wu earned his Ph.D. in statistics from the University of California, Berkeley (1990), and is also Adjunct Professor at the Georgetown University School of Medicine. He served as Associate Editor for Biometrics and Statistics in Medicine, and reviewer for National Science Foundation, NIH, and the U.S. Department of Veterans Affairs. Xin Tian earned her Ph.D. in statistics from Rutgers, the State University of New Jersey (2003). She has served on various NIH committees and collaborated extensively with clinical researchers.

This book covers the application of algebraic inequalities for reliability improvement and for uncertainty and risk reduction. It equips readers with powerful domain-independent methods for reducing risk based on algebraic inequalities and demonstrates the significant benefits derived from the application for risk and uncertainty reduction. Algebraic inequalities: * Provide a powerful reliability improvement, risk and uncertainty reduction method that transcends engineering and can be applied in various domains of human activity * Present an effective tool for dealing with deep uncertainty related to key reliability-critical parameters of systems and processes * Permit meaningful interpretations which link abstract inequalities with the real world * Offer a tool for determining tight bounds for the variation of risk-critical parameters and complying the design with these bounds to avoid failure * Allow optimising designs and processes by minimising the deviation of critical output parameters from their specified values and maximising their performance This book is primarily for engineering professionals and academic researchers in virtually all existing engineering disciplines.