ROC CURVES FOR CONTINUOUS DATA CHAPMAN HALL CRC MONOGRAPHS ON STATISTICS APPLIED PROBABILITY

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Roc Curves For Continuous Data

Author : Wojtek J. Krzanowski
ISBN : 1439800227
Genre : Business & Economics
File Size : 80.62 MB
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Since ROC curves have become ubiquitous in many application areas, the various advances have been scattered across disparate articles and texts. ROC Curves for Continuous Data is the first book solely devoted to the subject, bringing together all the relevant material to provide a clear understanding of how to analyze ROC curves. The fundamental theory of ROC curves The book first discusses the relationship between the ROC curve and numerous performance measures and then extends the theory into practice by describing how ROC curves are estimated. Further building on the theory, the authors present statistical tests for ROC curves and their summary statistics. They consider the impact of covariates on ROC curves, examine the important special problem of comparing two ROC curves, and cover Bayesian methods for ROC analysis. Special topics The text then moves on to extensions of the basic analysis to cope with more complex situations, such as the combination of multiple ROC curves and problems induced by the presence of more than two classes. Focusing on design and interpretation issues, it covers missing data, verification bias, sample size determination, the design of ROC studies, and the choice of optimum threshold from the ROC curve. The final chapter explores applications that not only illustrate some of the techniques but also demonstrate the very wide applicability of these techniques across different disciplines. With nearly 5,000 articles published to date relating to ROC analysis, the explosive interest in ROC curves and their analysis will continue in the foreseeable future. Embracing this growth of interest, this timely book will undoubtedly guide present and future users of ROC analysis.
Category: Business & Economics

Statistical Evaluation Of Diagnostic Performance

Author : Kelly H. Zou
ISBN : 9781439812235
Genre : Mathematics
File Size : 48.84 MB
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Statistical evaluation of diagnostic performance in general and Receiver Operating Characteristic (ROC) analysis in particular are important for assessing the performance of medical tests and statistical classifiers, as well as for evaluating predictive models or algorithms. This book presents innovative approaches in ROC analysis, which are relevant to a wide variety of applications, including medical imaging, cancer research, epidemiology, and bioinformatics. Statistical Evaluation of Diagnostic Performance: Topics in ROC Analysis covers areas including monotone-transformation techniques in parametric ROC analysis, ROC methods for combined and pooled biomarkers, Bayesian hierarchical transformation models, sequential designs and inferences in the ROC setting, predictive modeling, multireader ROC analysis, and free-response ROC (FROC) methodology. The book is suitable for graduate-level students and researchers in statistics, biostatistics, epidemiology, public health, biomedical engineering, radiology, medical imaging, biomedical informatics, and other closely related fields. Additionally, clinical researchers and practicing statisticians in academia, industry, and government could benefit from the presentation of such important and yet frequently overlooked topics.
Category: Mathematics

Analyzing Receiver Operating Characteristic Curves With Sas

Author : Mithat Gonen
ISBN : 9781629597966
Genre : Mathematics
File Size : 57.38 MB
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As a diagnostic decision-making tool, receiver operating characteristic (ROC) curves provide a comprehensive and visually attractive way to summarize the accuracy of predictions. They are used extensively in medical diagnosis and increasingly in fields such as data mining, credit scoring, weather forecasting, and psychometry. In Analyzing Receiver Operating Characteristic Curves with SAS, author Mithat Gonen illustrates the many existing SAS procedures that can be tailored to produce ROC curves and expands upon further analyses using other SAS procedures and macros. Both parametric and nonparametric methods for analyzing ROC curves are covered in detail. Topics addressed include: Appropriate methods for binary, ordinal, and continuous measures Computations using PROC FREQ, PROC LOGISTIC, PROC NLMIXED, and macros Comparing the ROC curves of several markers and adjusting them for covariates ROC curves with censored data Using the ROC curve for evaluating multivariable prediction models via bootstrap and cross-validation ROC curves in SAS Enterprise Miner And more! Written for any statistician interested in learning more about ROC curve methodology, the book assumes readers have a basic understanding of regression procedures and moderate familiarity with Base SAS and SAS/STAT. Some familiarity with SAS/GRAPH is helpful but not essential. This book is part of the SAS Press program.
Category: Mathematics

The Statistical Evaluation Of Medical Tests For Classification And Prediction

Author : Margaret Sullivan Pepe
ISBN : 9780198509844
Genre : Mathematics
File Size : 79.25 MB
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This book describes statistical techniques for the design and evaluation of research studies on medical diagnostic tests, screening tests, biomarkers and new technologies for classification and prediction in medicine. Based on solid mathematical theory, the book includes worked examples along with data and code, which provides the reader with easy implementation of methods.
Category: Mathematics

Statistical Methods In Diagnostic Medicine

Author : Xiao-Hua Zhou
ISBN : 9781118626047
Genre : Medical
File Size : 71.4 MB
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Praise for the First Edition " . . . the book is a valuable addition to the literature in the field, serving as a much-needed guide for both clinicians and advanced students."—Zentralblatt MATH A new edition of the cutting-edge guide to diagnostic tests in medical research In recent years, a considerable amount of research has focused on evolving methods for designing and analyzing diagnostic accuracy studies. Statistical Methods in Diagnostic Medicine, Second Edition continues to provide a comprehensive approach to the topic, guiding readers through the necessary practices for understanding these studies and generalizing the results to patient populations. Following a basic introduction to measuring test accuracy and study design, the authors successfully define various measures of diagnostic accuracy, describe strategies for designing diagnostic accuracy studies, and present key statistical methods for estimating and comparing test accuracy. Topics new to the Second Edition include: Methods for tests designed to detect and locate lesions Recommendations for covariate-adjustment Methods for estimating and comparing predictive values and sample size calculations Correcting techniques for verification and imperfect standard biases Sample size calculation for multiple reader studies when pilot data are available Updated meta-analysis methods, now incorporating random effects Three case studies thoroughly showcase some of the questions and statistical issues that arise in diagnostic medicine, with all associated data provided in detailed appendices. A related web site features Fortran, SAS®, and R software packages so that readers can conduct their own analyses. Statistical Methods in Diagnostic Medicine, Second Edition is an excellent supplement for biostatistics courses at the graduate level. It also serves as a valuable reference for clinicians and researchers working in the fields of medicine, epidemiology, and biostatistics.
Category: Medical

Circular And Linear Regression

Author : Nikolai Chernov
ISBN : 9781439835913
Genre : Computers
File Size : 73.29 MB
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Find the right algorithm for your image processing application Exploring the recent achievements that have occurred since the mid-1990s, Circular and Linear Regression: Fitting Circles and Lines by Least Squares explains how to use modern algorithms to fit geometric contours (circles and circular arcs) to observed data in image processing and computer vision. The author covers all facets—geometric, statistical, and computational—of the methods. He looks at how the numerical algorithms relate to one another through underlying ideas, compares the strengths and weaknesses of each algorithm, and illustrates how to combine the algorithms to achieve the best performance. After introducing errors-in-variables (EIV) regression analysis and its history, the book summarizes the solution of the linear EIV problem and highlights its main geometric and statistical properties. It next describes the theory of fitting circles by least squares, before focusing on practical geometric and algebraic circle fitting methods. The text then covers the statistical analysis of curve and circle fitting methods. The last chapter presents a sample of "exotic" circle fits, including some mathematically sophisticated procedures that use complex numbers and conformal mappings of the complex plane. Essential for understanding the advantages and limitations of the practical schemes, this book thoroughly addresses the theoretical aspects of the fitting problem. It also identifies obscure issues that may be relevant in future research.
Category: Computers

Generalized Linear Models Second Edition

Author : P. McCullagh
ISBN : 0412317605
Genre : Mathematics
File Size : 56.37 MB
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The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and other applications. The authors focus on examining the way a response variable depends on a combination of explanatory variables, treatment, and classification variables. They give particular emphasis to the important case where the dependence occurs through some unknown, linear combination of the explanatory variables. The Second Edition includes topics added to the core of the first edition, including conditional and marginal likelihood methods, estimating equations, and models for dispersion effects and components of dispersion. The discussion of other topics-log-linear and related models, log odds-ratio regression models, multinomial response models, inverse linear and related models, quasi-likelihood functions, and model checking-was expanded and incorporates significant revisions. Comprehension of the material requires simply a knowledge of matrix theory and the basic ideas of probability theory, but for the most part, the book is self-contained. Therefore, with its worked examples, plentiful exercises, and topics of direct use to researchers in many disciplines, Generalized Linear Models serves as ideal text, self-study guide, and reference.
Category: Mathematics

Nonparametric Statistics On Manifolds And Their Applications To Object Data Analysis

Author : Victor Patrangenaru
ISBN : 9781439820513
Genre : Mathematics
File Size : 61.36 MB
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A New Way of Analyzing Object Data from a Nonparametric Viewpoint Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis provides one of the first thorough treatments of the theory and methodology for analyzing data on manifolds. It also presents in-depth applications to practical problems arising in a variety of fields, including statistics, medical imaging, computer vision, pattern recognition, and bioinformatics. The book begins with a survey of illustrative examples of object data before moving to a review of concepts from mathematical statistics, differential geometry, and topology. The authors next describe theory and methods for working on various manifolds, giving a historical perspective of concepts from mathematics and statistics. They then present problems from a wide variety of areas, including diffusion tensor imaging, similarity shape analysis, directional data analysis, and projective shape analysis for machine vision. The book concludes with a discussion of current related research and graduate-level teaching topics as well as considerations related to computational statistics. Researchers in diverse fields must combine statistical methodology with concepts from projective geometry, differential geometry, and topology to analyze data objects arising from non-Euclidean object spaces. An expert-driven guide to this approach, this book covers the general nonparametric theory for analyzing data on manifolds, methods for working with specific spaces, and extensive applications to practical research problems. These problems show how object data analysis opens a formidable door to the realm of big data analysis.
Category: Mathematics

Sequential Analysis

Author : Alexander Tartakovsky
ISBN : 9781439838211
Genre : Mathematics
File Size : 50.43 MB
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Sequential Analysis: Hypothesis Testing and Changepoint Detection systematically develops the theory of sequential hypothesis testing and quickest changepoint detection. It also describes important applications in which theoretical results can be used efficiently. The book reviews recent accomplishments in hypothesis testing and changepoint detection both in decision-theoretic (Bayesian) and non-decision-theoretic (non-Bayesian) contexts. The authors not only emphasize traditional binary hypotheses but also substantially more difficult multiple decision problems. They address scenarios with simple hypotheses and more realistic cases of two and finitely many composite hypotheses. The book primarily focuses on practical discrete-time models, with certain continuous-time models also examined when general results can be obtained very similarly in both cases. It treats both conventional i.i.d. and general non-i.i.d. stochastic models in detail, including Markov, hidden Markov, state-space, regression, and autoregression models. Rigorous proofs are given for the most important results. Written by leading authorities in the field, this book covers the theoretical developments and applications of sequential hypothesis testing and sequential quickest changepoint detection in a wide range of engineering and environmental domains. It explains how the theoretical aspects influence the hypothesis testing and changepoint detection problems as well as the design of algorithms.
Category: Mathematics

The Top Ten Algorithms In Data Mining

Author : Xindong Wu
ISBN : 142008965X
Genre : Computers
File Size : 83.66 MB
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Identifying some of the most influential algorithms that are widely used in the data mining community, The Top Ten Algorithms in Data Mining provides a description of each algorithm, discusses its impact, and reviews current and future research. Thoroughly evaluated by independent reviewers, each chapter focuses on a particular algorithm and is written by either the original authors of the algorithm or world-class researchers who have extensively studied the respective algorithm. The book concentrates on the following important algorithms: C4.5, k-Means, SVM, Apriori, EM, PageRank, AdaBoost, kNN, Naive Bayes, and CART. Examples illustrate how each algorithm works and highlight its overall performance in a real-world application. The text covers key topics—including classification, clustering, statistical learning, association analysis, and link mining—in data mining research and development as well as in data mining, machine learning, and artificial intelligence courses. By naming the leading algorithms in this field, this book encourages the use of data mining techniques in a broader realm of real-world applications. It should inspire more data mining researchers to further explore the impact and novel research issues of these algorithms.
Category: Computers