"If mathematical modeling is the process of turning real phenomena into mathematical abstractions, then numerical computation is largely about the transformation from abstract mathematics to concrete reality. Many science and engineering disciplines have long benefited from the tremendous value of the correspondence between quantitative information and mathematical manipulation." -from the Preface Fundamentals of Numerical Computation is an advanced undergraduate-level introduction to the mathematics and use of algorithms for the fundamental problems of numerical computation: linear algebra, finding roots, approximating data and functions, and solving differential equations. The book is organized with simpler methods in the first half and more advanced methods in the second half, allowing use for either a single course or a sequence of two courses. The authors take readers from basic to advanced methods, illustrating them with over 200 self-contained MATLAB functions and examples designed for those with no prior MATLAB experience. Although the text provides many examples, exercises, and illustrations, the aim of the authors is not to provide a cookbook per se, but rather an exploration of the principles of cooking. Professors Driscoll and Braun have developed an online resource that includes well-tested materials related to every chapter. Among these materials are lecture-related slides and videos, ideas for student projects, laboratory exercises, computational examples and scripts, and all the functions presented in the book.

A unique point of this book is its low threshold, textually simple and at the same time full of self-assessment opportunities. Other unique points are the succinctness of the chapters with 3 to 6 pages, the presence of entire-commands-texts of the statistical methodologies reviewed and the fact that dull scientific texts imposing an unnecessary burden on busy and jaded professionals have been left out. For readers requesting more background, theoretical and mathematical information a note section with references is in each chapter. The first edition in 2010 was the first publication of a complete overview of SPSS methodologies for medical and health statistics. Well over 100,000 copies of various chapters were sold within the first year of publication. Reasons for a rewrite were four. First, many important comments from readers urged for a rewrite. Second, SPSS has produced many updates and upgrades, with relevant novel and improved methodologies. Third, the authors felt that the chapter texts needed some improvements for better readability: chapters have now been classified according the outcome data helpful for choosing your analysis rapidly, a schematic overview of data, and explanatory graphs have been added. Fourth, current data are increasingly complex and many important methods for analysis were missing in the first edition. For that latter purpose some more advanced methods seemed unavoidable, like hierarchical loglinear methods, gamma and Tweedie regressions and random intercept analyses. In order for the contents of the book to remain covered by the title, the authors renamed the book: SPSS for Starters and 2nd Levelers. Special care was, nonetheless, taken to keep things as simple as possible, simple menu commands are given. The arithmetic is still of a no-more-than high-school level. Step-by-step analyses of different statistical methodologies are given with the help of 60 SPSS data files available through the internet. Because of the lack of time of this busy group of people, the authors have given every effort to produce a text as succinct as possible.

"Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, "provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new sections, in addition to fully-updated examples, tables, figures, and a revised appendix. Intended primarily for practitioners, this book does not require sophisticated mathematical skills or deep understanding of the underlying theory and methods nor does it discuss alternative technologies for reasoning under uncertainty. The theory and methods presented are illustrated through more than 140 examples, and exercises are included for the reader to check his or her level of understanding. The techniques and methods presented for knowledge elicitation, model construction and verification, modeling techniques and tricks, learning models from data, and analyses of models have all been developed and refined on the basis of numerous courses that the authors have held for practitioners worldwide. "

By the end of this book, the reader will understand: the difficulties of finding a needle in a haystack; creative solutions to address the problem; unique ways of engineering features and solving the problem of the lack of data (e.g. synthetic data). Additionally, the reader will be able to: avoid mistakes resulting from a lack of understanding; search for appropriate methods of feature engineering; locate the relevant technological solutions within the general context of decision-making.

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.

This book provides a general introduction to Sequential Monte Carlo (SMC) methods, also known as particle filters. These methods have become a staple for the sequential analysis of data in such diverse fields as signal processing, epidemiology, machine learning, population ecology, quantitative finance, and robotics. The coverage is comprehensive, ranging from the underlying theory to computational implementation, methodology, and diverse applications in various areas of science. This is achieved by describing SMC algorithms as particular cases of a general framework, which involves concepts such as Feynman-Kac distributions, and tools such as importance sampling and resampling. This general framework is used consistently throughout the book. Extensive coverage is provided on sequential learning (filtering, smoothing) of state-space (hidden Markov) models, as this remains an important application of SMC methods. More recent applications, such as parameter estimation of these models (through e.g. particle Markov chain Monte Carlo techniques) and the simulation of challenging probability distributions (in e.g. Bayesian inference or rare-event problems), are also discussed. The book may be used either as a graduate text on Sequential Monte Carlo methods and state-space modeling, or as a general reference work on the area. Each chapter includes a set of exercises for self-study, a comprehensive bibliography, and a "Python corner," which discusses the practical implementation of the methods covered. In addition, the book comes with an open source Python library, which implements all the algorithms described in the book, and contains all the programs that were used to perform the numerical experiments.

This book provides comprehensive coverage of the field of outlier analysis from a computer science point of view. It integrates methods from data mining, machine learning, and statistics within the computational framework and therefore appeals to multiple communities. The chapters of this book can be organized into three categories: Basic algorithms: Chapters 1 through 7 discuss the fundamental algorithms for outlier analysis, including probabilistic and statistical methods, linear methods, proximity-based methods, high-dimensional (subspace) methods, ensemble methods, and supervised methods. Domain-specific methods: Chapters 8 through 12 discuss outlier detection algorithms for various domains of data, such as text, categorical data, time-series data, discrete sequence data, spatial data, and network data. Applications: Chapter 13 is devoted to various applications of outlier analysis. Some guidance is also provided for the practitioner. The second edition of this book is more detailed and is written to appeal to both researchers and practitioners. Significant new material has been added on topics such as kernel methods, one-class support-vector machines, matrix factorization, neural networks, outlier ensembles, time-series methods, and subspace methods. It is written as a textbook and can be used for classroom teaching.

Immediately implementable code, with extensive and varied illustrations of graph variants and layouts. Examples and exercises across a variety of real-life contexts including business, politics, education, social media and crime investigation. Dedicated chapter on graph visualization methods. Practical walkthroughs of common methodological uses: finding influential actors in groups, discovering hidden community structures, facilitating diverse interaction in organizations, detecting political alignment, determining what influences connection and attachment. Various downloadable data sets for use both in class and individual learning projects. Final chapter dedicated to individual or group project examples.

Immediately implementable code, with extensive and varied illustrations of graph variants and layouts. Examples and exercises across a variety of real-life contexts including business, politics, education, social media and crime investigation. Dedicated chapter on graph visualization methods. Practical walkthroughs of common methodological uses: finding influential actors in groups, discovering hidden community structures, facilitating diverse interaction in organizations, detecting political alignment, determining what influences connection and attachment. Various downloadable data sets for use both in class and individual learning projects. Final chapter dedicated to individual or group project examples.

This book covers using R for doing optimization, a key area of operations research, which has been applied to virtually every industry. The focus is on linear and mixed integer optimization. It uses an algebraic modeling approach for creating formulations that pairs naturally with an algebraic implementation in R. With the rapid rise of interest in data analytics, a data analytics platform is key. Working technology and business professionals need an awareness of the tools and language of data analysis. R reduces the barrier to entry for people to start using data analytics tools. Philosophically, the book emphasizes creating formulations before going into implementation. Algebraic representation allows for clear understanding and generalization of large applications, and writing formulations is necessary to explain and convey the modeling decisions made. Appendix A introduces R. Mathematics is used at the level of subscripts and summations Refreshers are provided in Appendix B. This book: * Provides and explains code so examples are relatively clear and self-contained. * Emphasizes creating algebraic formulations before implementing. * Focuses on application rather than algorithmic details. * Embodies the philosophy of reproducible research. * Uses open-source tools to ensure access to powerful optimization tools. * Promotes open-source: all materials are available on the author's github repository. * Demonstrates common debugging practices with a troubleshooting emphasis specific to optimization modeling using R. * Provides code readers can adapt to their own applications . This book can be used for graduate and undergraduate courses for students without a background in optimization and with varying mathematical backgrounds.

This book presents a theoretical and practical overview of computational modeling in bioengineering, focusing on a range of applications including electrical stimulation of neural and cardiac tissue, implantable drug delivery, cancer therapy, biomechanics, cardiovascular dynamics, as well as fluid-structure interaction for modelling of organs, tissues, cells and devices. It covers the basic principles of modeling and simulation with ordinary and partial differential equations using MATLAB and COMSOL Multiphysics numerical software. The target audience primarily comprises postgraduate students and researchers, but the book may also be beneficial for practitioners in the medical device industry.

A comprehensive introduction to various numerical methods used in computational finance today

Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and calibration of specific financial instruments and models. It features a strong emphasis on robust schemes for the numerical treatment of problems within computational finance. Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration of financial models to market data, Monte Carlo and Quasi Monte Carlo techniques for simulating high dimensional systems, and local and global optimization tools to solve the minimization problem.

This book describes Python3 programming resources for implementing decision aiding algorithms in the context of a bipolar-valued outranking approach. These computing resources, made available under the name Digraph3, are useful in the field of Algorithmic Decision Theory and more specifically in outranking-based Multiple-Criteria Decision Aiding (MCDA). The first part of the book presents a set of tutorials introducing the Digraph3 collection of Python3 modules and its main objects, such as bipolar-valued digraphs and outranking digraphs. In eight methodological chapters, the second part illustrates multiple-criteria evaluation models and decision algorithms. These chapters are largely problem-oriented and demonstrate how to edit a new multiple-criteria performance tableau, how to build a best choice recommendation, how to compute the winner of an election and how to make rankings or ratings using incommensurable criteria. The book's third part presents three real-world decision case studies, while the fourth part addresses more advanced topics, such as computing ordinal correlations between bipolar-valued outranking digraphs, computing kernels in bipolar-valued digraphs, testing for confidence or stability of outranking statements when facing uncertain or solely ordinal criteria significance weights, and tempering plurality tyranny effects in social choice problems. The fifth and last part is more specifically focused on working with undirected graphs, tree graphs and forests. The closing chapter explores comparability, split, interval and permutation graphs. The book is primarily intended for graduate students in management sciences, computational statistics and operations research. The chapters presenting algorithms for ranking multicriteria performance records will be of computational interest for designers of web recommender systems. Similarly, the relative and absolute quantile-rating algorithms, discussed and illustrated in several chapters, will be of practical interest to public and private performance auditors.

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.

Now in its second edition, Text Analysis with R provides a practical introduction to computational text analysis using the open source programming language R. R is an extremely popular programming language, used throughout the sciences; due to its accessibility, R is now used increasingly in other research areas. In this volume, readers immediately begin working with text, and each chapter examines a new technique or process, allowing readers to obtain a broad exposure to core R procedures and a fundamental understanding of the possibilities of computational text analysis at both the micro and the macro scale. Each chapter builds on its predecessor as readers move from small scale "microanalysis" of single texts to large scale "macroanalysis" of text corpora, and each concludes with a set of practice exercises that reinforce and expand upon the chapter lessons. The book's focus is on making the technical palatable and making the technical useful and immediately gratifying. Text Analysis with R is written with students and scholars of literature in mind but will be applicable to other humanists and social scientists wishing to extend their methodological toolkit to include quantitative and computational approaches to the study of text. Computation provides access to information in text that readers simply cannot gather using traditional qualitative methods of close reading and human synthesis. This new edition features two new chapters: one that introduces dplyr and tidyr in the context of parsing and analyzing dramatic texts to extract speaker and receiver data, and one on sentiment analysis using the syuzhet package. It is also filled with updated material in every chapter to integrate new developments in the field, current practices in R style, and the use of more efficient algorithms.

*Systematically introducing major components of SPM process. *Novel hybrid methods (228 hybrids plus numerous variants) of modern statistical methods or machine learning methods with mathematical and/or univariate geostatistical methods. *Novel predictive accuracy-based variable selection techniques for spatial predictive methods. *Predictive accuracy-based parameter/model optimization. *Reproducible examples for SPM of various data types in R.

The fun and friendly guide to mastering IBM's Statistical Package for the Social Sciences Written by an author team with a combined 55 years of experience using SPSS, this updated guide takes the guesswork out of the subject and helps you get the most out of using the leader in predictive analysis. Covering the latest release and updates to SPSS 27.0, and including more than 150 pages of basic statistical theory, it helps you understand the mechanics behind the calculations, perform predictive analysis, produce informative graphs, and more. You'll even dabble in programming as you expand SPSS functionality to suit your specific needs. Master the fundamental mechanics of SPSS Learn how to get data into and out of the program Graph and analyze your data more accurately and efficiently Program SPSS with Command Syntax Get ready to start handling data like a pro--with step-by-step instruction and expert advice!

Coherent treatment of a variety of approaches to multiple comparisons Broad coverage of topics, with contributions by internationally leading experts Detailed treatment of applications in medicine and life sciences Suitable for researchers, lecturers / students, and practitioners

R Visualizations: Derive Meaning from Data focuses on one of the two major topics of data analytics: data visualization, a.k.a., computer graphics. In the book, major R systems for visualization are discussed, organized by topic and not by system. Anyone doing data analysis will be shown how to use R to generate any of the basic visualizations with the R visualization systems. Further, this book introduces the author's lessR system, which always can accomplish a visualization with less coding than the use of other systems, sometimes dramatically so, and also provides accompanying statistical analyses. Key Features Presents thorough coverage of the leading R visualization system, ggplot2. Gives specific guidance on using base R graphics to attain visualizations of the same quality as those provided by ggplot2. Shows how to create a wide range of data visualizations: distributions of categorical and continuous variables, many types of scatterplots including with a third variable, time series, and maps. Inclusion of the various approaches to R graphics organized by topic instead of by system. Presents the recent work on interactive visualization in R. David W. Gerbing received his PhD from Michigan State University in 1979 in quantitative analysis, and currently is a professor of quantitative analysis in the School of Business at Portland State University. He has published extensively in the social and behavioral sciences with a focus on quantitative methods. His lessR package has been in development since 2009.

Improve Your Analytical Skills Incorporating the latest R packages as well as new case studies and applications, Using R and RStudio for Data Management, Statistical Analysis, and Graphics, Second Edition covers the aspects of R most often used by statistical analysts. New users of R will find the book's simple approach easy to understand while more sophisticated users will appreciate the invaluable source of task-oriented information. New to the Second Edition The use of RStudio, which increases the productivity of R users and helps users avoid error-prone cut-and-paste workflows New chapter of case studies illustrating examples of useful data management tasks, reading complex files, making and annotating maps, "scraping" data from the web, mining text files, and generating dynamic graphics New chapter on special topics that describes key features, such as processing by group, and explores important areas of statistics, including Bayesian methods, propensity scores, and bootstrapping New chapter on simulation that includes examples of data generated from complex models and distributions A detailed discussion of the philosophy and use of the knitr and markdown packages for R New packages that extend the functionality of R and facilitate sophisticated analyses Reorganized and enhanced chapters on data input and output, data management, statistical and mathematical functions, programming, high-level graphics plots, and the customization of plots Easily Find Your Desired Task Conveniently organized by short, clear descriptive entries, this edition continues to show users how to easily perform an analytical task in R. Users can quickly find and implement the material they need through the extensive indexing, cross-referencing, and worked examples in the text. Datasets and code are available for download on a supplementary website.

* Provides a comprehensive review of methods and applications of Bayesian variable selection. * Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. * Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. * Includes contributions by experts in the field.