Chapman & Hall/CRC Computer Science & Data Analysis – serie

A new and refreshingly different approach to presenting the foundations of statistical algorithms, Foundations of Statistical Algorithms: With References to R Packages reviews the historical development of basic algorithms to illuminate the evolution of today’s more powerful statistical algorithms. It emphasizes recurring themes in all statistical algorithms, including computation, assessment and verification, iteration, intuition, randomness, repetition and parallelization, and scalability. Unique in scope, the book reviews the upcoming challenge of scaling many of the established techniques to very large data sets and delves into systematic verification by demonstrating how to derive general classes of worst case inputs and emphasizing the importance of testing over a large number of different inputs. Broadly accessible, the book offers examples, exercises, and selected solutions in each chapter as well as access to a supplementary website. After working through the material covered in the book, readers should not only understand current algorithms but also gain a deeper understanding of how algorithms are constructed, how to evaluate new algorithms, which recurring principles are used to tackle some of the tough problems statistical programmers face, and how to take an idea for a new method and turn it into something practically useful.

The rapid advancement in the theoretical understanding of statistical and machine learning methods for semisupervised learning has made it difficult for nonspecialists to keep up to date in the field. Providing a broad, accessible treatment of the theory as well as linguistic applications, Semisupervised Learning for Computational Linguistics offers self-contained coverage of semisupervised methods that includes background material on supervised and unsupervised learning.The book presents a brief history of semisupervised learning and its place in the spectrum of learning methods before moving on to discuss well-known natural language processing methods, such as self-training and co-training. It then centers on machine learning techniques, including the boundary-oriented methods of perceptrons, boosting, support vector machines (SVMs), and the null-category noise model. In addition, the book covers clustering, the expectation-maximization (EM) algorithm, related generative methods, and agreement methods. It concludes with the graph-based method of label propagation as well as a detailed discussion of spectral methods.Taking an intuitive approach to the material, this lucid book facilitates the application of semisupervised learning methods to natural language processing and provides the framework and motivation for a more systematic study of machine learning.

Developed by Jean-Paul Benzérci more than 30 years ago, correspondence analysis as a framework for analyzing data quickly found widespread popularity in Europe. The topicality and importance of correspondence analysis continue, and with the tremendous computing power now available and new fields of application emerging, its significance is greater than ever.Correspondence Analysis and Data Coding with Java and R clearly demonstrates why this technique remains important and in the eyes of many, unsurpassed as an analysis framework. After presenting some historical background, the author presents a theoretical overview of the mathematics and underlying algorithms of correspondence analysis and hierarchical clustering. The focus then shifts to data coding, with a survey of the widely varied possibilities correspondence analysis offers and introduction of the Java software for correspondence analysis, clustering, and interpretation tools. A chapter of case studies follows, wherein the author explores applications to areas such as shape analysis and time-evolving data. The final chapter reviews the wealth of studies on textual content as well as textual form, carried out by Benzécri and his research lab. These discussions show the importance of correspondence analysis to artificial intelligence as well as to stylometry and other fields.This book not only shows why correspondence analysis is important, but with a clear presentation replete with advice and guidance, also shows how to put this technique into practice. Downloadable software and data sets allow quick, hands-on exploration of innovative correspondence analysis applications.

Pattern Recognition Algorithms for Data Mining addresses different pattern recognition (PR) tasks in a unified framework with both theoretical and experimental results. Tasks covered include data condensation, feature selection, case generation, clustering/classification, and rule generation and evaluation. This volume presents various theories, methodologies, and algorithms, using both classical approaches and hybrid paradigms. The authors emphasize large datasets with overlapping, intractable, or nonlinear boundary classes, and datasets that demonstrate granular computing in soft frameworks.Organized into eight chapters, the book begins with an introduction to PR, data mining, and knowledge discovery concepts. The authors analyze the tasks of multi-scale data condensation and dimensionality reduction, then explore the problem of learning with support vector machine (SVM). They conclude by highlighting the significance of granular computing for different mining tasks in a soft paradigm.

INLA stands for Integrated Nested Laplace Approximations, which is a new method for fitting a broad class of Bayesian regression models. No samples of the posterior marginal distributions need to be drawn using INLA, so it is a computationally convenient alternative to Markov chain Monte Carlo (MCMC), the standard tool for Bayesian inference.Bayesian Regression Modeling with INLA covers a wide range of modern regression models and focuses on the INLA technique for building Bayesian models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to demonstrate the interplay of theory and practice with reproducible studies. Complete R commands are provided for each example, and a supporting website holds all of the data described in the book. An R package including the data and additional functions in the book is available to download. The book is aimed at readers who have a basic knowledge of statistical theory and Bayesian methodology. It gets readers up to date on the latest in Bayesian inference using INLA and prepares them for sophisticated, real-world work.

Written by some major contributors to the development of this class of graphical models, Chain Event Graphs introduces a viable and straightforward new tool for statistical inference, model selection and learning techniques. The book extends established technologies used in the study of discrete Bayesian Networks so that they apply in a much more general settingAs the first book on Chain Event Graphs, this monograph is expected to become a landmark work on the use of event trees and coloured probability trees in statistics, and to lead to the increased use of such tree models to describe hypotheses about how events might unfold.Features:introduces a new and exciting discrete graphical model based on an event treefocusses on illustrating inferential techniques, making its methodology accessible to a very broad audience and, most importantly, to practitionersillustrated by a wide range of examples, encompassing important present and future applicationsincludes exercises to test comprehension and can easily be used as a course bookintroduces relevant software packages

Computer simulations based on mathematical models have become ubiquitous across the engineering disciplines and throughout the physical sciences. Successful use of a simulation model, however, requires careful interrogation of the model through systematic computer experiments. While specific theoretical/mathematical examinations of computer experiment design are available, those interested in applying proposed methodologies need a practical presentation and straightforward guidance on analyzing and interpreting experiment results.Written by authors with strong academic reputations and real-world practical experience, Design and Modeling for Computer Experiments is exactly the kind of treatment you need. The authors blend a sound, modern statistical approach with extensive engineering applications and clearly delineate the steps required to successfully model a problem and provide an analysis that will help find the solution. Part I introduces the design and modeling of computer experiments and the basic concepts used throughout the book. Part II focuses on the design of computer experiments. The authors present the most popular space-filling designs - like Latin hypercube sampling and its modifications and uniform design - including their definitions, properties, construction and related generating algorithms. Part III discusses the modeling of data from computer experiments. Here the authors present various modeling techniques and discuss model interpretation, including sensitivity analysis. An appendix reviews the statistics and mathematics concepts needed, and numerous examples clarify the techniques and their implementation.The complexity of real physical systems means that there is usually no simple analytic formula that sufficiently describes the phenomena. Useful both as a textbook and professional reference, this book presents the techniques you need to design and model computer experiments for practical problem solving.

"Data Science Foundations is most welcome and, indeed, a piece of literature that the field is very much in need of…quite different from most data analytics texts which largely ignore foundational concepts and simply present a cookbook of methods…a very useful text and I would certainly use it in my teaching."- Mark Girolami, Warwick UniversityData Science encompasses the traditional disciplines of mathematics, statistics, data analysis, machine learning, and pattern recognition. This book is designed to provide a new framework for Data Science, based on a solid foundation in mathematics and computational science. It is written in an accessible style, for readers who are engaged with the subject but not necessarily experts in all aspects. It includes a wide range of case studies from diverse fields, and seeks to inspire and motivate the reader with respect to data, associated information, and derived knowledge.

Full of real-world case studies and practical advice, Exploratory Multivariate Analysis by Example Using R, Second Edition focuses on four fundamental methods of multivariate exploratory data analysis that are most suitable for applications. It covers principal component analysis (PCA) when variables are quantitative, correspondence analysis (CA) and multiple correspondence analysis (MCA) when variables are categorical, and hierarchical cluster analysis.The authors take a geometric point of view that provides a unified vision for exploring multivariate data tables. Within this framework, they present the principles, indicators, and ways of representing and visualising objects that are common to the exploratory methods. The authors show how to use categorical variables in a PCA context in which variables are quantitative, how to handle more than two categorical variables in a CA context in which there are originally two variables, and how to add quantitative variables in an MCA context in which variables are categorical. They also illustrate the methods using examples from various fields, with related R code accessible in the FactoMineR package developed by the authors.

This book provides a comprehensive overview of music data analysis, from introductory material to advanced concepts. It covers various applications including transcription and segmentation as well as chord and harmony, instrument and tempo recognition. It also discusses the implementation aspects of music data analysis such as architecture, user interface and hardware. It is ideal for use in university classes with an interest in music data analysis. It also could be used in computer science and statistics as well as musicology.

The beginning of the age of artificial intelligence and machine learning has created new challenges and opportunities for data analysts, statisticians, mathematicians, econometricians, computer scientists and many others. At the root of these techniques are algorithms and methods for clustering and classifying different types of large datasets, including time series data.Time Series Clustering and Classification includes relevant developments on observation-based, feature-based and model-based traditional and fuzzy clustering methods, feature-based and model-based classification methods, and machine learning methods. It presents a broad and self-contained overview of techniques for both researchers and students.FeaturesProvides an overview of the methods and applications of pattern recognition of time series Covers a wide range of techniques, including unsupervised and supervised approaches Includes a range of real examples from medicine, finance, environmental science, and more R and MATLAB code, and relevant data sets are available on a supplementary website

Textual Statistics with R comprehensively covers the main multidimensional methods in textual statistics supported by a specially-written package in R. Methods discussed include correspondence analysis, clustering, and multiple factor analysis for contigency tables. Each method is illuminated by applications. The book is aimed at researchers and students in statistics, social sciences, hiistory, literature and linguistics. The book will be of interest to anyone from practitioners needing to extract information from texts to students in the field of massive data, where the ability to process textual data is becoming essential.

Geometric Data Analysis designates the approach of Multivariate Statistics that conceptualizes the set of observations as a Euclidean cloud of points. Combinatorial Inference in Geometric Data Analysis gives an overview of multidimensional statistical inference methods applicable to clouds of points that make no assumption on the process of generating data or distributions, and that are not based on random modelling but on permutation procedures recasting in a combinatorial framework. It focuses particularly on the comparison of a group of observations to a reference population (combinatorial test) or to a reference value of a location parameter (geometric test), and on problems of homogeneity, that is the comparison of several groups for two basic designs. These methods involve the use of combinatorial procedures to build a reference set in which we place the data. The chosen test statistics lead to original extensions, such as the geometric interpretation of the observed level, and the construction of a compatibility region.Features: Defines precisely the object under study in the context of multidimensional procedures, that is clouds of points Presents combinatorial tests and related computations with R and Coheris SPAD software Includes four original case studies to illustrate application of the tests Includes necessary mathematical background to ensure it is self–contained This book is suitable for researchers and students of multivariate statistics, as well as applied researchers of various scientific disciplines. It could be used for a specialized course taught at either master or PhD level.

Praise for the Second Edition:"The authors present an intuitive and easy-to-read book. … accompanied by many examples, proposed exercises, good references, and comprehensive appendices that initiate the reader unfamiliar with MATLAB."—Adolfo Alvarez Pinto, International Statistical Review "Practitioners of EDA who use MATLAB will want a copy of this book. … The authors have done a great service by bringing together so many EDA routines, but their main accomplishment in this dynamic text is providing the understanding and tools to do EDA.—David A Huckaby, MAA ReviewsExploratory Data Analysis (EDA) is an important part of the data analysis process. The methods presented in this text are ones that should be in the toolkit of every data scientist. As computational sophistication has increased and data sets have grown in size and complexity, EDA has become an even more important process for visualizing and summarizing data before making assumptions to generate hypotheses and models. Exploratory Data Analysis with MATLAB, Third Edition presents EDA methods from a computational perspective and uses numerous examples and applications to show how the methods are used in practice. The authors use MATLAB code, pseudo-code, and algorithm descriptions to illustrate the concepts. The MATLAB code for examples, data sets, and the EDA Toolbox are available for download on the book’s website.New to the Third Edition Random projections and estimating local intrinsic dimensionality Deep learning autoencoders and stochastic neighbor embedding Minimum spanning tree and additional cluster validity indices Kernel density estimation Plots for visualizing data distributions, such as beanplots and violin plots A chapter on visualizing categorical data

A Strong Practical Focus on Applications and AlgorithmsComputational Statistics Handbook with MATLAB®, Third Edition covers today’s most commonly used techniques in computational statistics while maintaining the same philosophy and writing style of the bestselling previous editions. The text keeps theoretical concepts to a minimum, emphasizing the implementation of the methods.New to the Third EditionThis third edition is updated with the latest version of MATLAB and the corresponding version of the Statistics and Machine Learning Toolbox. It also incorporates new sections on the nearest neighbor classifier, support vector machines, model checking and regularization, partial least squares regression, and multivariate adaptive regression splines.Web ResourceThe authors include algorithmic descriptions of the procedures as well as examples that illustrate the use of algorithms in data analysis. The MATLAB code, examples, and data sets are available online.

Updated and expanded, Bayesian Artificial Intelligence, Second Edition provides a practical and accessible introduction to the main concepts, foundation, and applications of Bayesian networks. It focuses on both the causal discovery of networks and Bayesian inference procedures. Adopting a causal interpretation of Bayesian networks, the authors discuss the use of Bayesian networks for causal modeling. They also draw on their own applied research to illustrate various applications of the technology.New to the Second Edition New chapter on Bayesian network classifiersNew section on object-oriented Bayesian networksNew section that addresses foundational problems with causal discovery and Markov blanket discoveryNew section that covers methods of evaluating causal discovery programsDiscussions of many common modeling errorsNew applications and case studiesMore coverage on the uses of causal interventions to understand and reason with causal Bayesian networks Illustrated with real case studies, the second edition of this bestseller continues to cover the groundwork of Bayesian networks. It presents the elements of Bayesian network technology, automated causal discovery, and learning probabilities from data and shows how to employ these technologies to develop probabilistic expert systems.Web ResourceThe book’s website at www.csse.monash.edu.au/bai/book/book.html offers a variety of supplemental materials, including example Bayesian networks and data sets. Instructors can email the authors for sample solutions to many of the problems in the text.

To harness the high-throughput potential of DNA microarray technology, it is crucial that the analysis stages of the process are decoupled from the requirements of operator assistance. Microarray Image Analysis: An Algorithmic Approach presents an automatic system for microarray image processing to make this decoupling a reality. The proposed system integrates and extends traditional analytical-based methods and custom-designed novel algorithms.The book first explores a new technique that takes advantage of a multiview approach to image analysis and addresses the challenges of applying powerful traditional techniques, such as clustering, to full-scale microarray experiments. It then presents an effective feature identification approach, an innovative technique that renders highly detailed surface models, a new approach to subgrid detection, a novel technique for the background removal process, and a useful technique for removing "noise." The authors also develop an expectation–maximization (EM) algorithm for modeling gene regulatory networks from gene expression time series data. The final chapter describes the overall benefits of these techniques in the biological and computer sciences and reviews future research topics.This book systematically brings together the fields of image processing, data analysis, and molecular biology to advance the state of the art in this important area. Although the text focuses on improving the processes involved in the analysis of microarray image data, the methods discussed can be applied to a broad range of medical and computer vision analysis areas.

Providing key information on how to work with research data, Introduction to Data Technologies presents ideas and techniques for performing critical, behind-the-scenes tasks that take up so much time and effort yet typically receive little attention in formal education. With a focus on computational tools, the book shows readers how to improve their awareness of what tasks can be achieved and describes the correct approach to perform these tasks. Practical examples demonstrate the most important pointsThe author first discusses how to write computer code using HTML as a concrete example. He then covers a variety of data storage topics, including different file formats, XML, and the structure and design issues of relational databases. After illustrating how to extract data from a relational database using SQL, the book presents tools and techniques for searching, sorting, tabulating, and manipulating data. It also introduces some very basic programming concepts as well as the R language for statistical computing. Each of these topics has supporting chapters that offer reference material on HTML, CSS, XML, DTD, SQL, R, and regular expressions.One-stop shop of introductory computing information Written by a member of the R Development Core Team, this resource shows readers how to apply data technologies to tasks within a research setting. Collecting material otherwise scattered across many books and the web, it explores how to publish information via the web, how to access information stored in different formats, and how to write small programs to automate simple, repetitive tasks.

Full of real-world case studies and practical advice, Exploratory Multivariate Analysis by Example Using R, Second Edition focuses on four fundamental methods of multivariate exploratory data analysis that are most suitable for applications. It covers principal component analysis (PCA) when variables are quantitative, correspondence analysis (CA) and multiple correspondence analysis (MCA) when variables are categorical, and hierarchical cluster analysis.The authors take a geometric point of view that provides a unified vision for exploring multivariate data tables. Within this framework, they present the principles, indicators, and ways of representing and visualising objects that are common to the exploratory methods. The authors show how to use categorical variables in a PCA context in which variables are quantitative, how to handle more than two categorical variables in a CA context in which there are originally two variables, and how to add quantitative variables in an MCA context in which variables are categorical. They also illustrate the methods using examples from various fields, with related R code accessible in the FactoMineR package developed by the authors.

Fulfilling the need for a practical user's guide, Statistics in MATLAB: A Primer provides an accessible introduction to the latest version of MATLAB and its extensive functionality for statistics. Assuming a basic knowledge of statistics and probability as well as a fundamental understanding of linear algebra concepts, this book covers capabilities in the main MATLAB package and the Statistics Toolbox. The student version of MATLAB presents examples of how MATLAB can be used to analyze data and offers access to a companion website with data sets and additional examples. It contains figures and visual aids to assist in application of the software and explains how to determine what method should be used for analysis. Statistics in MATLAB: A Primer is an ideal reference for undergraduate and graduate students in engineering, mathematics, statistics, economics, biostatistics, and computer science. It is also appropriate for a diverse professional market, making it a valuable addition to the libraries of researchers in statistics, computer science, data mining, machine learning, image analysis, signal processing, and engineering.

Textual Statistics with R comprehensively covers the main multidimensional methods in textual statistics supported by a specially-written package in R. Methods discussed include correspondence analysis, clustering, and multiple factor analysis for contigency tables. Each method is illuminated by applications. The book is aimed at researchers and students in statistics, social sciences, hiistory, literature and linguistics. The book will be of interest to anyone from practitioners needing to extract information from texts to students in the field of massive data, where the ability to process textual data is becoming essential.

Due to its data handling and modeling capabilities as well as its flexibility, R is becoming the most widely used software in bioinformatics. R Programming for Bioinformatics explores the programming skills needed to use this software tool for the solution of bioinformatics and computational biology problems.Drawing on the author’s first-hand experiences as an expert in R, the book begins with coverage on the general properties of the R language, several unique programming aspects of R, and object-oriented programming in R. It presents methods for data input and output as well as database interactions. The author also examines different facets of string handling and manipulations, discusses the interfacing of R with other languages, and describes how to write software packages. He concludes with a discussion on the debugging and profiling of R code.With numerous examples and exercises, this practical guide focuses on developing R programming skills in order to tackle problems encountered in bioinformatics and computational biology.

Providing key information on how to work with research data, Introduction to Data Technologies presents ideas and techniques for performing critical, behind-the-scenes tasks that take up so much time and effort yet typically receive little attention in formal education. With a focus on computational tools, the book shows readers how to improve their awareness of what tasks can be achieved and describes the correct approach to perform these tasks. Practical examples demonstrate the most important pointsThe author first discusses how to write computer code using HTML as a concrete example. He then covers a variety of data storage topics, including different file formats, XML, and the structure and design issues of relational databases. After illustrating how to extract data from a relational database using SQL, the book presents tools and techniques for searching, sorting, tabulating, and manipulating data. It also introduces some very basic programming concepts as well as the R language for statistical computing. Each of these topics has supporting chapters that offer reference material on HTML, CSS, XML, DTD, SQL, R, and regular expressions.One-stop shop of introductory computing information Written by a member of the R Development Core Team, this resource shows readers how to apply data technologies to tasks within a research setting. Collecting material otherwise scattered across many books and the web, it explores how to publish information via the web, how to access information stored in different formats, and how to write small programs to automate simple, repetitive tasks.

Updated and expanded, Bayesian Artificial Intelligence, Second Edition provides a practical and accessible introduction to the main concepts, foundation, and applications of Bayesian networks. It focuses on both the causal discovery of networks and Bayesian inference procedures. Adopting a causal interpretation of Bayesian networks, the authors discuss the use of Bayesian networks for causal modeling. They also draw on their own applied research to illustrate various applications of the technology.New to the Second Edition New chapter on Bayesian network classifiersNew section on object-oriented Bayesian networksNew section that addresses foundational problems with causal discovery and Markov blanket discoveryNew section that covers methods of evaluating causal discovery programsDiscussions of many common modeling errorsNew applications and case studiesMore coverage on the uses of causal interventions to understand and reason with causal Bayesian networksIllustrated with real case studies, the second edition of this bestseller continues to cover the groundwork of Bayesian networks. It presents the elements of Bayesian network technology, automated causal discovery, and learning probabilities from data and shows how to employ these technologies to develop probabilistic expert systems.Web ResourceThe book’s website at www.csse.monash.edu.au/bai/book/book.html offers a variety of supplemental materials, including example Bayesian networks and data sets. Instructors can email the authors for sample solutions to many of the problems in the text.

Visualization and Verbalization of Data shows how correspondence analysis and related techniques enable the display of data in graphical form, which results in the verbalization of the structures in data. Renowned researchers in the field trace the history of these techniques and cover their current applications.The first part of the book explains the historical origins of correspondence analysis and associated methods. The second part concentrates on the contributions made by the school of Jean-Paul Benzécri and related movements, such as social space and geometric data analysis. Although these topics are viewed from a French perspective, the book makes them understandable to an international audience.Throughout the text, well-known experts illustrate the use of the methods in practice. Examples include the spatial visualization of multivariate data, cluster analysis in computer science, the transformation of a textual data set into numerical data, the use of quantitative and qualitative variables in multiple factor analysis, different possibilities of recoding data prior to visualization, and the application of duality diagram theory to the analysis of a contingency table.

A Strong Practical Focus on Applications and AlgorithmsComputational Statistics Handbook with MATLAB®, Third Edition covers today’s most commonly used techniques in computational statistics while maintaining the same philosophy and writing style of the bestselling previous editions. The text keeps theoretical concepts to a minimum, emphasizing the implementation of the methods.New to the Third EditionThis third edition is updated with the latest version of MATLAB and the corresponding version of the Statistics and Machine Learning Toolbox. It also incorporates new sections on the nearest neighbor classifier, support vector machines, model checking and regularization, partial least squares regression, and multivariate adaptive regression splines.Web ResourceThe authors include algorithmic descriptions of the procedures as well as examples that illustrate the use of algorithms in data analysis. The MATLAB code, examples, and data sets are available online.

Fulfilling the need for a practical user’s guide, Statistics in MATLAB: A Primer provides an accessible introduction to the latest version of MATLAB® and its extensive functionality for statistics. Assuming a basic knowledge of statistics and probability as well as a fundamental understanding of linear algebra concepts, this book:Covers capabilities in the main MATLAB package, the Statistics Toolbox, and the student version of MATLABPresents examples of how MATLAB can be used to analyze dataOffers access to a companion website with data sets and additional examplesContains figures and visual aids to assist in application of the softwareExplains how to determine what method should be used for analysisStatistics in MATLAB: A Primer is an ideal reference for undergraduate and graduate students in engineering, mathematics, statistics, economics, biostatistics, and computer science. It is also appropriate for a diverse professional market, making it a valuable addition to the libraries of researchers in statistics, computer science, data mining, machine learning, image analysis, signal processing, and engineering.

This book provides a comprehensive overview of music data analysis, from introductory material to advanced concepts. It covers various applications including transcription and segmentation as well as chord and harmony, instrument and tempo recognition. It also discusses the implementation aspects of music data analysis such as architecture, user interface and hardware. It is ideal for use in university classes with an interest in music data analysis. It also could be used in computer science and statistics as well as musicology.

INLA stands for Integrated Nested Laplace Approximations, which is a new method for fitting a broad class of Bayesian regression models. No samples of the posterior marginal distributions need to be drawn using INLA, so it is a computationally convenient alternative to Markov chain Monte Carlo (MCMC), the standard tool for Bayesian inference.Bayesian Regression Modeling with INLA covers a wide range of modern regression models and focuses on the INLA technique for building Bayesian models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to demonstrate the interplay of theory and practice with reproducible studies. Complete R commands are provided for each example, and a supporting website holds all of the data described in the book. An R package including the data and additional functions in the book is available to download.The book is aimed at readers who have a basic knowledge of statistical theory and Bayesian methodology. It gets readers up to date on the latest in Bayesian inference using INLA and prepares them for sophisticated, real-world work.Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic.Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York.Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.