This book discusses a variety of methods for outlier ensembles and organizes them by the specific principles with which accuracy improvements are achieved. In addition, it covers the techniques with which such methods can be made more effective. A formal classification of these methods is provided, and the circumstances in which they work well are examined. The authors cover how outlier ensembles relate (both theoretically and practically) to the ensemble techniques used commonly for other data mining problems like classification. The similarities and (subtle) differences in the ensemble techniques for the classification and outlier detection problems are explored. These subtle differences do impact the design of ensemble algorithms for the latter problem. This book can be used for courses in data mining and related curricula. Many illustrative examples and exercises are provided in order to facilitate classroom teaching. A familiarity is assumed to the outlier detection problem and also to generic problem of ensemble analysis in classification. This is because many of the ensemble methods discussed in this book are adaptations from their counterparts in the classification domain. Some techniques explained in this book, such as wagging, randomized feature weighting, and geometric subsampling, provide new insights that are not available elsewhere. Also included is an analysis of the performance of various types of base detectors and their relative effectiveness. The book is valuable for researchers and practitioners for leveraging ensemble methods into optimal algorithmic design.

This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response transformations for multiple linear regression or experimental design models. This text is for graduates and undergraduates with a strong mathematical background. The prerequisites for this text are linear algebra and a calculus based course in statistics.

This book is a selection of peer-reviewed contributions presented at the third Bayesian Young Statisticians Meeting, BAYSM 2016, Florence, Italy, June 19-21. The meeting provided a unique opportunity for young researchers, M.S. students, Ph.D. students, and postdocs dealing with Bayesian statistics to connect with the Bayesian community at large, to exchange ideas, and to network with others working in the same field. The contributions develop and apply Bayesian methods in a variety of fields, ranging from the traditional (e.g., biostatistics and reliability) to the most innovative ones (e.g., big data and networks).

Marking the 30th anniversary of the European Conference on Modelling and Simulation (ECMS), this inspirational text/reference reviews significant advances in the field of modelling and simulation, as well as key applications of simulation in other disciplines. The broad-ranging volume presents contributions from a varied selection of distinguished experts chosen from high-impact keynote speakers and best paper winners from the conference, including a Nobel Prize recipient, and the first president of the European Council for Modelling and Simulation (also abbreviated to ECMS). This authoritative book will be of great value to all researchers working in the field of modelling and simulation, in addition to scientists from other disciplines who make use of modelling and simulation approaches in their work.

This book contains a rich set of tools for nonparametric analyses, and the purpose of this text is to provide guidance to students and professional researchers on how R is used for nonparametric data analysis in the biological sciences: To introduce when nonparametric approaches to data analysis are appropriate To introduce the leading nonparametric tests commonly used in biostatistics and how R is used to generate appropriate statistics for each test To introduce common figures typically associated with nonparametric data analysis and how R is used to generate appropriate figures in support of each data set The book focuses on how R is used to distinguish between data that could be classified as nonparametric as opposed to data that could be classified as parametric, with both approaches to data classification covered extensively. Following an introductory lesson on nonparametric statistics for the biological sciences, the book is organized into eight self-contained lessons on various analyses and tests using R to broadly compare differences between data sets and statistical approach.

This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are explained. Each section includes a set of exercises on the respective topics. Various functions and tools for the analysis of discrete survival data are collected in the R package discSurv that accompanies the book.

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

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

This textbook examines empirical linguistics from a theoretical linguist's perspective. It provides both a theoretical discussion of what quantitative corpus linguistics entails and detailed, hands-on, step-by-step instructions to implement the techniques in the field. The statistical methodology and R-based coding from this book teach readers the basic and then more advanced skills to work with large data sets in their linguistics research and studies. Massive data sets are now more than ever the basis for work that ranges from usage-based linguistics to the far reaches of applied linguistics. This book presents much of the methodology in a corpus-based approach. However, the corpus-based methods in this book are also essential components of recent developments in sociolinguistics, historical linguistics, computational linguistics, and psycholinguistics. Material from the book will also be appealing to researchers in digital humanities and the many non-linguistic fields that use textual data analysis and text-based sensorimetrics. Chapters cover topics including corpus processing, frequencing data, and clustering methods. Case studies illustrate each chapter with accompanying data sets, R code, and exercises for use by readers. This book may be used in advanced undergraduate courses, graduate courses, and self-study.

This book offers a collection of recent contributions and emerging ideas in the areas of robust statistics presented at the International Conference on Robust Statistics 2015 (ICORS 2015) held in Kolkata during 12-16 January, 2015. The book explores the applicability of robust methods in other non-traditional areas which includes the use of new techniques such as skew and mixture of skew distributions, scaled Bregman divergences, and multilevel functional data methods; application areas being circular data models and prediction of mortality and life expectancy. The contributions are of both theoretical as well as applied in nature. Robust statistics is a relatively young branch of statistical sciences that is rapidly emerging as the bedrock of statistical analysis in the 21st century due to its flexible nature and wide scope. Robust statistics supports the application of parametric and other inference techniques over a broader domain than the strictly interpreted model scenarios employed in classical statistical methods. The aim of the ICORS conference, which is being organized annually since 2001, is to bring together researchers interested in robust statistics, data analysis and related areas. The conference is meant for theoretical and applied statisticians, data analysts from other fields, leading experts, junior researchers and graduate students. The ICORS meetings offer a forum for discussing recent advances and emerging ideas in statistics with a focus on robustness, and encourage informal contacts and discussions among all the participants. They also play an important role in maintaining a cohesive group of international researchers interested in robust statistics and related topics, whose interactions transcend the meetings and endure year round.

This book is a valuable read for a diverse group of researchers and practitioners who analyze assessment data and construct test instruments. It focuses on the use of classical test theory (CTT) and item response theory (IRT), which are often required in the fields of psychology (e.g. for measuring psychological traits), health (e.g. for measuring the severity of disorders), and education (e.g. for measuring student performance), and makes these analytical tools accessible to a broader audience. Having taught assessment subjects to students from diverse backgrounds for a number of years, the three authors have a wealth of experience in presenting educational measurement topics, in-depth concepts and applications in an accessible format. As such, the book addresses the needs of readers who use CTT and IRT in their work but do not necessarily have an extensive mathematical background. The book also sheds light on common misconceptions in applying measurement models, and presents an integrated approach to different measurement methods, such as contrasting CTT with IRT and multidimensional IRT models with unidimensional IRT models. Wherever possible, comparisons between models are explicitly made. In addition, the book discusses concepts for test equating and differential item functioning, as well as Bayesian IRT models and plausible values using simple examples. This book can serve as a textbook for introductory courses on educational measurement, as supplementary reading for advanced courses, or as a valuable reference guide for researchers interested in analyzing student assessment data.

This focuses on the developing field of building probability models with the power of symbolic algebra systems. The book combines the uses of symbolic algebra with probabilistic/stochastic application and highlights the applications in a variety of contexts. The research explored in each chapter is unified by the use of A Probability Programming Language (APPL) to achieve the modeling objectives. APPL, as a research tool, enables a probabilist or statistician the ability to explore new ideas, methods, and models. Furthermore, as an open-source language, it sets the foundation for future algorithms to augment the original code. Computational Probability Applications is comprised of fifteen chapters, each presenting a specific application of computational probability using the APPL modeling and computer language. The chapter topics include using inverse gamma as a survival distribution, linear approximations of probability density functions, and also moment-ratio diagrams for univariate distributions. These works highlight interesting examples, often done by undergraduate students and graduate students that can serve as templates for future work. In addition, this book should appeal to researchers and practitioners in a range of fields including probability, statistics, engineering, finance, neuroscience, and economics.

This book has a collection of articles written by Big Data experts to describe some of the cutting-edge methods and applications from their respective areas of interest, and provides the reader with a detailed overview of the field of Big Data Analytics as it is practiced today. The chapters cover technical aspects of key areas that generate and use Big Data such as management and finance; medicine and healthcare; genome, cytome and microbiome; graphs and networks; Internet of Things; Big Data standards; bench-marking of systems; and others. In addition to different applications, key algorithmic approaches such as graph partitioning, clustering and finite mixture modelling of high-dimensional data are also covered. The varied collection of themes in this volume introduces the reader to the richness of the emerging field of Big Data Analytics.

This volume collects selected, peer-reviewed contributions from the 2nd Conference of the International Society for Nonparametric Statistics (ISNPS), held in Cadiz (Spain) between June 11-16 2014, and sponsored by the American Statistical Association, the Institute of Mathematical Statistics, the Bernoulli Society for Mathematical Statistics and Probability, the Journal of Nonparametric Statistics and Universidad Carlos III de Madrid. The 15 articles are a representative sample of the 336 contributed papers presented at the conference. They cover topics such as high-dimensional data modelling, inference for stochastic processes and for dependent data, nonparametric and goodness-of-fit testing, nonparametric curve estimation, object-oriented data analysis, and semiparametric inference. The aim of the ISNPS 2014 conference was to bring together recent advances and trends in several areas of nonparametric statistics in order to facilitate the exchange of research ideas, promote collaboration among researchers from around the globe, and contribute to the further development of the field.

This book enables readers who may not be familiar with matrices to understand a variety of multivariate analysis procedures in matrix forms. Another feature of the book is that it emphasizes what model underlies a procedure and what objective function is optimized for fitting the model to data. The author believes that the matrix-based learning of such models and objective functions is the fastest way to comprehend multivariate data analysis. The text is arranged so that readers can intuitively capture the purposes for which multivariate analysis procedures are utilized: plain explanations of the purposes with numerical examples precede mathematical descriptions in almost every chapter. This volume is appropriate for undergraduate students who already have studied introductory statistics. Graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis will also find the book useful, as it is based on modern matrix formulations with a special emphasis on singular value decomposition among theorems in matrix algebra. The book begins with an explanation of fundamental matrix operations and the matrix expressions of elementary statistics, followed by the introduction of popular multivariate procedures with advancing levels of matrix algebra chapter by chapter. This organization of the book allows readers without knowledge of matrices to deepen their understanding of multivariate data analysis.

The revised Fourth Edition of this popular textbook is redesigned with Excel 2016 to encourage business students to develop competitive advantages for use in their future careers as decision makers. Students learn to build models using logic and experience, produce statistics using Excel 2016 with shortcuts, and translate results into implications for decision makers. The textbook features new examples and assignments on global markets, including cases featuring Chipotle and Costco. A number of examples focus on business in emerging global markets with particular emphasis on emerging markets in Latin America, China, and India. Results are linked to implications for decision making with sensitivity analyses to illustrate how alternate scenarios can be compared. The author emphasises communicating results effectively in plain English and with screenshots and compelling graphics in the form of memos and PowerPoints. Chapters include screenshots to make it easy to conduct analyses in Excel 2016. PivotTables and PivotCharts, used frequently in business, are introduced from the start. The Fourth Edition features Monte Carlo simulation in four chapters, as a tool to illustrate the range of possible outcomes from decision makers' assumptions and underlying uncertainties. Model building with regression is presented as a process, adding levels of sophistication, with chapters on multicollinearity and remedies, forecasting and model validation, auto-correlation and remedies, indicator variables to represent segment differences, and seasonality, structural shifts or shocks in time series models. Special applications in market segmentation and portfolio analysis are offered, and an introduction to conjoint analysis is included. Nonlinear models are motivated with arguments of diminishing or increasing marginal response.

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

The goal of this guide and manual is to provide a practical and brief overview of the theory on computerized adaptive testing (CAT) and multistage testing (MST) and to illustrate the methodologies and applications using R open source language and several data examples. Implementation relies on the R packages catR and mstR that have been already or are being developed by the first author (with the team) and that include some of the newest research algorithms on the topic. The book covers many topics along with the R-code: the basics of R, theoretical overview of CAT and MST, CAT designs, CAT assembly methodologies, CAT simulations, catR package, CAT applications, MST designs, IRT-based MST methodologies, tree-based MST methodologies, mstR package, and MST applications. CAT has been used in many large-scale assessments over recent decades, and MST has become very popular in recent years. R open source language also has become one of the most useful tools for applications in almost all fields, including business and education. Though very useful and popular, R is a difficult language to learn, with a steep learning curve. Given the obvious need for but with the complex implementation of CAT and MST, it is very difficult for users to simulate or implement CAT and MST. Until this manual, there has been no book for users to design and use CAT and MST easily and without expense; i.e., by using the free R software. All examples and illustrations are generated using predefined scripts in R language, available for free download from the book's website.

This book offers an original and broad exploration of the fundamental methods in Clustering and Combinatorial Data Analysis, presenting new formulations and ideas within this very active field. With extensive introductions, formal and mathematical developments and real case studies, this book provides readers with a deeper understanding of the mutual relationships between these methods, which are clearly expressed with respect to three facets: logical, combinatorial and statistical. Using relational mathematical representation, all types of data structures can be handled in precise and unified ways which the author highlights in three stages: Clustering a set of descriptive attributes Clustering a set of objects or a set of object categories Establishing correspondence between these two dual clusterings Tools for interpreting the reasons of a given cluster or clustering are also included. Foundations and Methods in Combinatorial and Statistical Data Analysis and Clustering will be a valuable resource for students and researchers who are interested in the areas of Data Analysis, Clustering, Data Mining and Knowledge Discovery.

This textbook provides an introduction to the free software Python and its use for statistical data analysis. It covers common statistical tests for continuous, discrete and categorical data, as well as linear regression analysis and topics from survival analysis and Bayesian statistics. Working code and data for Python solutions for each test, together with easy-to-follow Python examples, can be reproduced by the reader and reinforce their immediate understanding of the topic. With recent advances in the Python ecosystem, Python has become a popular language for scientific computing, offering a powerful environment for statistical data analysis and an interesting alternative to R. The book is intended for master and PhD students, mainly from the life and medical sciences, with a basic knowledge of statistics. As it also provides some statistics background, the book can be used by anyone who wants to perform a statistical data analysis.

This book discusses examples in parametric inference with R. Combining basic theory with modern approaches, it presents the latest developments and trends in statistical inference for students who do not have an advanced mathematical and statistical background. The topics discussed in the book are fundamental and common to many fields of statistical inference and thus serve as a point of departure for in-depth study. The book is divided into eight chapters: Chapter 1 provides an overview of topics on sufficiency and completeness, while Chapter 2 briefly discusses unbiased estimation. Chapter 3 focuses on the study of moments and maximum likelihood estimators, and Chapter 4 presents bounds for the variance. In Chapter 5, topics on consistent estimator are discussed. Chapter 6 discusses Bayes, while Chapter 7 studies some more powerful tests. Lastly, Chapter 8 examines unbiased and other tests. Senior undergraduate and graduate students in statistics and mathematics, and those who have taken an introductory course in probability, will greatly benefit from this book. Students are expected to know matrix algebra, calculus, probability and distribution theory before beginning this course. Presenting a wealth of relevant solved and unsolved problems, the book offers an excellent tool for teachers and instructors who can assign homework problems from the exercises, and students will find the solved examples hugely beneficial in solving the exercise problems.

The ability to summarise data, compare models and apply computer-based analysis tools are vital skills necessary for studying and working in the physical sciences. This textbook supports undergraduate students as they develop and enhance these skills. Introducing data analysis techniques, this textbook pays particular attention to the internationally recognised guidelines for calculating and expressing measurement uncertainty. This new edition has been revised to incorporate Excel (R) 2010. It also provides a practical approach to fitting models to data using non-linear least squares, a powerful technique which can be applied to many types of model. Worked examples using actual experimental data help students understand how the calculations apply to real situations. Over 200 in-text exercises and end-of-chapter problems give students the opportunity to use the techniques themselves and gain confidence in applying them. Answers to the exercises and problems are given at the end of the book.

This book presents a comprehensive study of multivariate time series with linear state space structure. The emphasis is put on both the clarity of the theoretical concepts and on efficient algorithms for implementing the theory. In particular, it investigates the relationship between VARMA and state space models, including canonical forms. It also highlights the relationship between Wiener-Kolmogorov and Kalman filtering both with an infinite and a finite sample. The strength of the book also lies in the numerous algorithms included for state space models that take advantage of the recursive nature of the models. Many of these algorithms can be made robust, fast, reliable and efficient. The book is accompanied by a MATLAB package called SSMMATLAB and a webpage presenting implemented algorithms with many examples and case studies. Though it lays a solid theoretical foundation, the book also focuses on practical application, and includes exercises in each chapter. It is intended for researchers and students working with linear state space models, and who are familiar with linear algebra and possess some knowledge of statistics.

This book covers all the topics found in introductory descriptive statistics courses, including simple linear regression and time series analysis, the fundamentals of inferential statistics (probability theory, random sampling and estimation theory), and inferential statistics itself (confidence intervals, testing). Each chapter starts with the necessary theoretical background, which is followed by a variety of examples. The core examples are based on the content of the respective chapter, while the advanced examples, designed to deepen students' knowledge, also draw on information and material from previous chapters. The enhanced online version helps students grasp the complexity and the practical relevance of statistical analysis through interactive examples and is suitable for undergraduate and graduate students taking their first statistics courses, as well as for undergraduate students in non-mathematical fields, e.g. economics, the social sciences etc.

This book features research contributions from The Abel Symposium on Statistical Analysis for High Dimensional Data, held in Nyvagar, Lofoten, Norway, in May 2014. The focus of the symposium was on statistical and machine learning methodologies specifically developed for inference in "big data" situations, with particular reference to genomic applications. The contributors, who are among the most prominent researchers on the theory of statistics for high dimensional inference, present new theories and methods, as well as challenging applications and computational solutions. Specific themes include, among others, variable selection and screening, penalised regression, sparsity, thresholding, low dimensional structures, computational challenges, non-convex situations, learning graphical models, sparse covariance and precision matrices, semi- and non-parametric formulations, multiple testing, classification, factor models, clustering, and preselection. Highlighting cutting-edge research and casting light on future research directions, the contributions will benefit graduate students and researchers in computational biology, statistics and the machine learning community.