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The development of powerful computing environment and the geographical information system (GIS) in recent decades has thrust the analysis of geo-referenced disease incidence data into the mainstream of spatial epidemiology. This book offers a modern perspective on statistical methods for detecting disease clustering, an indispensable procedure to find a statistical evidence on aetiology of the disease under study. With increasing public health concerns about environmental risks, the need for sophisticated methods for analyzing spatial health events is immediate. Furthermore, the research area of statistical methods for disease clustering now attracts a wide audience due to the perceived need to implement wide-ranging monitoring systems to detect possible health-related events such as the occurrence of the severe acute respiratory syndrome (SARS), pandemic influenza and bioterrorism As an invaluable resource for a wide range of audience including public health researchers, epidemiologists and biostatistians, this book features: A concise introduction to basic concepts of disease clustering/clusters A historical overview of methods for disease clustering A detailed treatment of selected methods useful for practical investigation of disease clustering Analysis and illustration of methods for a variety of real data sets Toshiro Tango, Ph.D., is the Director of Department of Technology Assessment and Biostatistics of National Institute of Public Health, Japan. He has published a number of methodological and applied articles on various aspects of biostatistics. He is Past President of the Japanese Region of the International Biometric Society. He has served as Associate Editor for several journals including Statistics in Medicine and Biometrics.

Mathematical statistics

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Computational techniques based on simulation have now become an essential part of the statistician's toolbox. It is thus crucial to provide statisticians with a practical understanding of those methods, and there is no better way to develop intuition and skills for simulation than to use simulation to solve statistical problems. Introducing Monte Carlo Methods with R covers the main tools used in statistical simulation from a programmer's point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison. While this book constitutes a comprehensive treatment of simulation methods, the theoretical justification of those methods has been considerably reduced, compared with Robert and Casella (2004). Similarly, the more exploratory and less stable solutions are not covered here. This book does not require a preliminary exposure to the R programming language or to Monte Carlo methods, nor an advanced mathematical background. While many examples are set within a Bayesian framework, advanced expertise in Bayesian statistics is not required. The book covers basic random generation algorithms, Monte Carlo techniques for integration and optimization, convergence diagnoses, Markov chain Monte Carlo methods, including Metropolis {Hastings and Gibbs algorithms, and adaptive algorithms. All chapters include exercises and all R programs are available as an R package called mcsm. The book appeals to anyone with a practical interest in simulation methods but no previous exposure. It is meant to be useful for students and practitioners in areas such as statistics, signal processing, communications engineering, control theory, econometrics, finance and more. The programming parts are introduced progressively to be accessible to any reader. Christian P. Robert is Professor of Statistics at Université Paris Dauphine, and Head of the Statistics Laboratory of CREST, both in Paris, France. He has authored more than 150 papers in applied probability, Bayesian statistics and simulation methods. He is a fellow of the Institute of Mathematical Statistics and the recipient of an IMS Medallion. He has authored eight other books, including The Bayesian Choice which received the ISBA DeGroot Prize in 2004, Monte Carlo Statistical Methods with George Casella, and Bayesian Core with Jean-Michel Marin. He has served as Joint Editor of the Journal of the Royal Statistical Society Series B, as well as an associate editor for most major statistical journals, and was the 2008 ISBA President. George Casella is Distinguished Professor in the Department of Statistics at the University of Florida. He is active in both theoretical and applied statistics, is a fellow of the Institute of Mathematical Statistics and the American Statistical Association, and a Foreign Member of the Spanish Royal Academy of Sciences. He has served as Theory and Methods Editor of the Journal of the American Statistical Association, as Executive Editor of Statistical Science, and as Joint Editor of the Journal of the Royal Statistical Society Series B. In addition to books with Christian Robert, he has written Variance Components, 1992, with S.R. Searle and C.E. McCulloch; Statistical Inference, Second Edition, 2001, with Roger Berger; and Theory of Point Estimation, Second Edition, 1998, with Erich Lehmann. His latest book is Statistical Design 2008.

Mathematical statistics

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The new edition of this influential textbook, geared towards graduate or advanced undergraduate students, teaches the statistics necessary for financial engineering. In doing so, it illustrates concepts using financial markets and economic data, R Labs with real-data exercises, and graphical and analytic methods for modeling and diagnosing modeling errors. Financial engineers now have access to enormous quantities of data. To make use of these data, the powerful methods in this book, particularly about volatility and risks, are essential. Strengths of this fully-revised edition include major additions to the R code and the advanced topics covered. Individual chapters cover, among other topics, multivariate distributions, copulas, Bayesian computations, risk management, multivariate volatility and cointegration. Suggested prerequisites are basic knowledge of statistics and probability, matrices and linear algebra, and calculus. There is an appendix on probability, statistics and linear algebra. Practicing financial engineers will also find this book of interest. David Ruppert is Andrew Schultz, Jr., Professor of Engineering and Professor of Statistical Science at Cornell University, where he teaches statistics and financial engineering and is a member of the Program in Financial Engineering. Professor Ruppert received his PhD in Statistics at Michigan State University. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics and won the Wilcoxon prize. He is Editor of the Journal of the American Statistical Association-Theory and Methods and former Editor of the Electronic Journal of Statistics and of the Institute of Mathematical Statistics's Lecture Notes—Monographs. Professor Ruppert has published over 125 scientific papers and four books: Transformation and Weighting in Regression, Measurement Error in Nonlinear Models, Semiparametric Regression, and Statistics and Finance: An Introduction. David S. Matteson is Assistant Professor of Statistical Science at Cornell University, where he is a member of the ILR School, Center for Applied Mathematics, Field of Operations Research, and the Program in Financial Engineering, and teaches statistics and financial engineering. Professor Matteson received his PhD in Statistics at the University of Chicago. He received a CAREER Award from the National Science Foundation and won Best Academic Paper Awards from the annual R/Finance conference. He is an Associate Editor of the Journal of the American Statistical Association-Theory and Methods, Biometrics, and Statistica Sinica. He is also an Officer for the Business and Economic Statistics Section of the American Statistical Association, and a member of the Institute of Mathematical Statistics and the International Biometric Society.

Mathematical statistics

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Mathematical statistics

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This highly anticipated second edition features new chapters and sections, 225 new references, and comprehensive R software. In keeping with the previous edition, this book is about the art and science of data analysis and predictive modeling, which entails choosing and using multiple tools. Instead of presenting isolated techniques, this text emphasizes problem solving strategies that address the many issues arising when developing multivariable models using real data and not standard textbook examples. It includes imputation methods for dealing with missing data effectively, methods for fitting nonlinear relationships and for making the estimation of transformations a formal part of the modeling process, methods for dealing with "too many variables to analyze and not enough observations," and powerful model validation techniques based on the bootstrap. The reader will gain a keen understanding of predictive accuracy, and the harm of categorizing continuous predictors or outcomes. This text realistically deals with model uncertainty, and its effects on inference, to achieve "safe data mining." It also presents many graphical methods for communicating complex regression models to non-statisticians. Regression Modeling Strategies presents full-scale case studies of non-trivial datasets instead of over-simplified illustrations of each method. These case studies use freely available R functions that make the multiple imputation, model building, validation, and interpretation tasks described in the book relatively easy to do. Most of the methods in this text apply to all regression models, but special emphasis is given to multiple regression using generalized least squares for longitudinal data, the binary logistic model, models for ordinal responses, parametric survival regression models, and the Cox semiparametric survival model. A new emphasis is given to the robust analysis of continuous dependent variables using ordinal regression. As in the first edition, this text is intended for Masters' or Ph.D. level graduate students who have had a general introductory probability and statistics course and who are well versed in ordinary multiple regression and intermediate algebra. The book will also serve as a reference for data analysts and statistical methodologists, as it contains an up-to-date survey and bibliography of modern statistical modeling techniques. Examples used in the text mostly come from biomedical research, but the methods are applicable anywhere predictive models ("analytics") are useful, including economics, epidemiology, sociology, psychology, engineering, and marketing.

Mathematical statistics