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 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.

Get an introduction to functional data structures using R and write more effective code and gain performance for your programs. This book teaches you workarounds because data in functional languages is not mutable: for example you'll learn how to change variable-value bindings by modifying environments, which can be exploited to emulate pointers and implement traditional data structures. You'll also see how, by abandoning traditional data structures, you can manipulate structures by building new versions rather than modifying them. You'll discover how these so-called functional data structures are different from the traditional data structures you might know, but are worth understanding to do serious algorithmic programming in a functional language such as R. By the end of Functional Data Structures in R, you'll understand the choices to make in order to most effectively work with data structures when you cannot modify the data itself. These techniques are especially applicable for algorithmic development important in big data, finance, and other data science applications. What You'll Learn Carry out algorithmic programming in R Use abstract data structures Work with both immutable and persistent data Emulate pointers and implement traditional data structures in R Build new versions of traditional data structures that are known Who This Book Is For Experienced or advanced programmers with at least a comfort level with R. Some experience with data structures recommended.

This textbook presents the basic concepts and methods of fluid mechanics, including Lagrangian and Eulerian descriptions, tensors of stresses and strains, continuity, momentum, energy, thermodynamics laws, and similarity theory. The models and their solutions are presented within a context of the mechanics of multiphase media. The treatment fully utilizes the computer algebra and software system Mathematica (R) to both develop concepts and help the reader to master modern methods of solving problems in fluid mechanics. Topics and features: Glossary of over thirty Mathematica (R) computer programs Extensive, self-contained appendix of Mathematica (R) functions and their use Chapter coverage of mechanics of multiphase heterogeneous media Detailed coverage of theory of shock waves in gas dynamics Thorough discussion of aerohydrodynamics of ideal and viscous fluids an d gases Complete worked examples with detailed solutions Problem-solving approach Foundations of Fluid Mechanics with Applications is a complete and accessible text or reference for graduates and professionals in mechanics, applied mathematics, physical sciences, materials science, and engineering. It is an essential resource for the study and use of modern solution methods for problems in fluid mechanics and the underlying mathematical models. The present, softcover reprint is designed to make this classic textbook available to a wider audience.

Technology/Engineering/Mechanical

Provides all the tools needed to begin solving optimization problems using MATLAB(R)

The Second Edition of Applied Optimization with MATLAB(R) Programming enables readers to harness all the features of MATLAB(R) to solve optimization problems using a variety of linear and nonlinear design optimization techniques. By breaking down complex mathematical concepts into simple ideas and offering plenty of easy-to-follow examples, this text is an ideal introduction to the field. Examples come from all engineering disciplines as well as science, economics, operations research, and mathematics, helping readers understand how to apply optimization techniques to solve actual problems.

This Second Edition has been thoroughly revised, incorporating current optimization techniques as well as the improved MATLAB(R) tools. Two important new features of the text are:

Introduction to the scan and zoom method, providing a simple, effective technique that works for unconstrained, constrained, and global optimization problems

New chapter, Hybrid Mathematics: An Application, using examples to illustrate how optimization can develop analytical or explicit solutions to differential systems and data-fitting problems

Each chapter ends with a set of problems that give readers an opportunity to put their new skills into practice. Almost all of the numerical techniques covered in the text are supported by MATLAB(R) code, which readers can download on the text's companion Web site www.wiley.com/go/venkat2e and use to begin solving problems on their own.

This text is recommended for upper-level undergraduate and graduate students in all areas of engineering as well as other disciplines that use optimization techniques to solve design problems.

Key features: Unique in its combination of serving as an introduction to spatial statistics and to modeling agricultural and ecological data using R Provides exercises in each chapter to facilitate the book's use as a course textbook or for self-study Adds new material on generalized additive models, point pattern analysis, and new methods of Bayesian analysis of spatial data. Includes a completely revised chapter on the analysis of spatiotemporal data featuring recently introduced software and methods Updates its coverage of R software including newly introduced packages Spatial Data Analysis in Ecology and Agriculture Using R, 2nd Edition provides practical instruction on the use of the R programming language to analyze spatial data arising from research in ecology, agriculture, and environmental science. Readers have praised the book's practical coverage of spatial statistics, real-world examples, and user-friendly approach in presenting and explaining R code, aspects maintained in this update. Using data sets from cultivated and uncultivated ecosystems, the book guides the reader through the analysis of each data set, including setting research objectives, designing the sampling plan, data quality control, exploratory and confirmatory data analysis, and drawing scientific conclusions. Additional material to accompany the book, on both analyzing satellite data and on multivariate analysis, can be accessed at https://www.plantsciences.ucdavis.edu/plant/additionaltopics.htm.

Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matern covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

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 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 book traces the theory and methodology of multivariate statistical analysis and shows how it can be conducted in practice using the LISREL computer program. It presents not only the typical uses of LISREL, such as confirmatory factor analysis and structural equation models, but also several other multivariate analysis topics, including regression (univariate, multivariate, censored, logistic, and probit), generalized linear models, multilevel analysis, and principal component analysis. It provides numerous examples from several disciplines and discusses and interprets the results, illustrated with sections of output from the LISREL program, in the context of the example. The book is intended for masters and PhD students and researchers in the social, behavioral, economic and many other sciences who require a basic understanding of multivariate statistical theory and methods for their analysis of multivariate data. It can also be used as a textbook on various topics of multivariate statistical analysis.

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 provides a unified view on a new methodology for Machine Translation (MT). This methodology extracts information from widely available resources (extensive monolingual corpora) while only assuming the existence of a very limited parallel corpus, thus having a unique starting point to Statistical Machine Translation (SMT). In this book, a detailed presentation of the methodology principles and system architecture is followed by a series of experiments, where the proposed system is compared to other MT systems using a set of established metrics including BLEU, NIST, Meteor and TER. Additionally, a free-to-use code is available, that allows the creation of new MT systems. The volume is addressed to both language professionals and researchers. Prerequisites for the readers are very limited and include a basic understanding of the machine translation as well as of the basic tools of natural language processing.

This comprehensive and richly illustrated volume provides up-to-date material on Singular Spectrum Analysis (SSA). SSA is a well-known methodology for the analysis and forecasting of time series. Since quite recently, SSA is also being used to analyze digital images and other objects that are not necessarily of planar or rectangular form and may contain gaps. SSA is multi-purpose and naturally combines both model-free and parametric techniques, which makes it a very special and attractive methodology for solving a wide range of problems arising in diverse areas, most notably those associated with time series and digital images. An effective, comfortable and accessible implementation of SSA is provided by the R-package Rssa, which is available from CRAN and reviewed in this book. Written by prominent statisticians who have extensive experience with SSA, the book (a) presents the up-to-date SSA methodology, including multidimensional extensions, in language accessible to a large circle of users, (b) combines different versions of SSA into a single tool, (c) shows the diverse tasks that SSA can be used for, (d) formally describes the main SSA methods and algorithms, and (e) provides tutorials on the Rssa package and the use of SSA. The book offers a valuable resource for a very wide readership, including professional statisticians, specialists in signal and image processing, as well as specialists in numerous applied disciplines interested in using statistical methods for time series analysis, forecasting, signal and image processing. The book is written on a level accessible to a broad audience and includes a wealth of examples; hence it can also be used as a textbook for undergraduate and postgraduate courses on time series analysis and signal processing.

This textbook on practical data analytics unites fundamental principles, algorithms, and data. Algorithms are the keystone of data analytics and the focal point of this textbook. Clear and intuitive explanations of the mathematical and statistical foundations make the algorithms transparent. But practical data analytics requires more than just the foundations. Problems and data are enormously variable and only the most elementary of algorithms can be used without modification. Programming fluency and experience with real and challenging data is indispensable and so the reader is immersed in Python and R and real data analysis. By the end of the book, the reader will have gained the ability to adapt algorithms to new problems and carry out innovative analyses. This book has three parts:(a) Data Reduction: Begins with the concepts of data reduction, data maps, and information extraction. The second chapter introduces associative statistics, the mathematical foundation of scalable algorithms and distributed computing. Practical aspects of distributed computing is the subject of the Hadoop and MapReduce chapter.(b) Extracting Information from Data: Linear regression and data visualization are the principal topics of Part II. The authors dedicate a chapter to the critical domain of Healthcare Analytics for an extended example of practical data analytics. The algorithms and analytics will be of much interest to practitioners interested in utilizing the large and unwieldly data sets of the Centers for Disease Control and Prevention's Behavioral Risk Factor Surveillance System.(c) Predictive Analytics Two foundational and widely used algorithms, k-nearest neighbors and naive Bayes, are developed in detail. A chapter is dedicated to forecasting. The last chapter focuses on streaming data and uses publicly accessible data streams originating from the Twitter API and the NASDAQ stock market in the tutorials. This book is intended for a one- or two-semester course in data analytics for upper-division undergraduate and graduate students in mathematics, statistics, and computer science. The prerequisites are kept low, and students with one or two courses in probability or statistics, an exposure to vectors and matrices, and a programming course will have no difficulty. The core material of every chapter is accessible to all with these prerequisites. The chapters often expand at the close with innovations of interest to practitioners of data science. Each chapter includes exercises of varying levels of difficulty. The text is eminently suitable for self-study and an exceptional resource for practitioners.

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 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 introduces multidimensional scaling (MDS) and unfolding as data analysis techniques for applied researchers. MDS is used for the analysis of proximity data on a set of objects, representing the data as distances between points in a geometric space (usually of two dimensions). Unfolding is a related method that maps preference data (typically evaluative ratings of different persons on a set of objects) as distances between two sets of points (representing the persons and the objects, resp.). This second edition has been completely revised to reflect new developments and the coverage of unfolding has also been substantially expanded. Intended for applied researchers whose main interests are in using these methods as tools for building substantive theories, it discusses numerous applications (classical and recent), highlights practical issues (such as evaluating model fit), presents ways to enforce theoretical expectations for the scaling solutions, and addresses the typical mistakes that MDS/unfolding users tend to make. Further, it shows how MDS and unfolding can be used in practical research work, primarily by using the smacof package in the R environment but also Proxscal in SPSS. It is a valuable resource for psychologists, social scientists, and market researchers, with a basic understanding of multivariate statistics (such as multiple regression and factor analysis).

Reproducible Finance with R: Code Flows and Shiny Apps for Portfolio Analysis is a unique introduction to data science for investment management that explores the three major R/finance coding paradigms, emphasizes data visualization, and explains how to build a cohesive suite of functioning Shiny applications. The full source code, asset price data and live Shiny applications are available at reproduciblefinance.com. The ideal reader works in finance or wants to work in finance and has a desire to learn R code and Shiny through simple, yet practical real-world examples. The book begins with the first step in data science: importing and wrangling data, which in the investment context means importing asset prices, converting to returns, and constructing a portfolio. The next section covers risk and tackles descriptive statistics such as standard deviation, skewness, kurtosis, and their rolling histories. The third section focuses on portfolio theory, analyzing the Sharpe Ratio, CAPM, and Fama French models. The book concludes with applications for finding individual asset contribution to risk and for running Monte Carlo simulations. For each of these tasks, the three major coding paradigms are explored and the work is wrapped into interactive Shiny dashboards.

This edited volume on the latest advances in data science covers a wide range of topics in the context of data analysis and classification. In particular, it includes contributions on classification methods for high-dimensional data, clustering methods, multivariate statistical methods, and various applications. The book gathers a selection of peer-reviewed contributions presented at the Fifteenth Conference of the International Federation of Classification Societies (IFCS2015), which was hosted by the Alma Mater Studiorum, University of Bologna, from July 5 to 8, 2015.

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 tutorial teaches you how to use the statistical programming language R to develop a business case simulation and analysis. It presents a methodology for conducting business case analysis that minimizes decision delay by focusing stakeholders on what matters most and suggests pathways for minimizing the risk in strategic and capital allocation decisions. Business case analysis, often conducted in spreadsheets, exposes decision makers to additional risks that arise just from the use of the spreadsheet environment. R has become one of the most widely used tools for reproducible quantitative analysis, and analysts fluent in this language are in high demand. The R language, traditionally used for statistical analysis, provides a more explicit, flexible, and extensible environment than spreadsheets for conducting business case analysis. The main tutorial follows the case in which a chemical manufacturing company considers constructing a chemical reactor and production facility to bring a new compound to market. There are numerous uncertainties and risks involved, including the possibility that a competitor brings a similar product online. The company must determine the value of making the decision to move forward and where they might prioritize their attention to make a more informed and robust decision. While the example used is a chemical company, the analysis structure it presents can be applied to just about any business decision, from IT projects to new product development to commercial real estate. The supporting tutorials include the perspective of the founder of a professional service firm who wants to grow his business and a member of a strategic planning group in a biomedical device company who wants to know how much to budget in order to refine the quality of information about critical uncertainties that might affect the value of a chosen product development pathway. What You'll Learn Set up a business case abstraction in an influence diagram to communicate the essence of the problem to other stakeholders Model the inherent uncertainties in the problem with Monte Carlo simulation using the R language Communicate the results graphically Draw appropriate insights from the results Develop creative decision strategies for thorough opportunity cost analysis Calculate the value of information on critical uncertainties between competing decision strategies to set the budget for deeper data analysis Construct appropriate information to satisfy the parameters for the Monte Carlo simulation when little or no empirical data are available Who This Book Is For Financial analysts, data practitioners, and risk/business professionals; also appropriate for graduate level finance, business, or data science students

The book provides a description of the process of health economic evaluation and modelling for cost-effectiveness analysis, particularly from the perspective of a Bayesian statistical approach. Some relevant theory and introductory concepts are presented using practical examples and two running case studies. The book also describes in detail how to perform health economic evaluations using the R package BCEA (Bayesian Cost-Effectiveness Analysis). BCEA can be used to post-process the results of a Bayesian cost-effectiveness model and perform advanced analyses producing standardised and highly customisable outputs. It presents all the features of the package, including its many functions and their practical application, as well as its user-friendly web interface. The book is a valuable resource for statisticians and practitioners working in the field of health economics wanting to simplify and standardise their workflow, for example in the preparation of dossiers in support of marketing authorisation, or academic and scientific publications.

This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier-Stokes equations, and systems of nonlinear advection-diffusion-reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.

This guide for practicing statisticians, data scientists, and R users and programmers will teach the essentials of preprocessing: data leveraging the R programming language to easily and quickly turn noisy data into usable pieces of information. Data wrangling, which is also commonly referred to as data munging, transformation, manipulation, janitor work, etc., can be a painstakingly laborious process. Roughly 80% of data analysis is spent on cleaning and preparing data; however, being a prerequisite to the rest of the data analysis workflow (visualization, analysis, reporting), it is essential that one become fluent and efficient in data wrangling techniques. This book will guide the user through the data wrangling process via a step-by-step tutorial approach and provide a solid foundation for working with data in R. The author's goal is to teach the user how to easily wrangle data in order to spend more time on understanding the content of the data. By the end of the book, the user will have learned: How to work with different types of data such as numerics, characters, regular expressions, factors, and dates The difference between different data structures and how to create, add additional components to, and subset each data structure How to acquire and parse data from locations previously inaccessible How to develop functions and use loop control structures to reduce code redundancy How to use pipe operators to simplify code and make it more readable How to reshape the layout of data and manipulate, summarize, and join data sets

After the fundamental volume and the advanced technique volume, this volume focuses on R applications in the quantitative investment area. Quantitative investment has been hot for some years, and there are more and more startups working on it, combined with many other internet communities and business models. R is widely used in this area, and can be a very powerful tool. The author introduces R applications with cases from his own startup, covering topics like portfolio optimization and risk management.