Markov Chain Monte Carlo Simulations and Their Statistical Analysis

Markov Chain Monte Carlo Simulations and Their Statistical Analysis

Author: Bernd A. Berg

Publisher: World Scientific

Published: 2004

Total Pages: 380

ISBN-13: 9812389350

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This book teaches modern Markov chain Monte Carlo (MC) simulation techniques step by step. The material should be accessible to advanced undergraduate students and is suitable for a course. It ranges from elementary statistics concepts (the theory behind MC simulations), through conventional Metropolis and heat bath algorithms, autocorrelations and the analysis of the performance of MC algorithms, to advanced topics including the multicanonical approach, cluster algorithms and parallel computing. Therefore, it is also of interest to researchers in the field. The book relates the theory directly to Web-based computer code. This allows readers to get quickly started with their own simulations and to verify many numerical examples easily. The present code is in Fortran 77, for which compilers are freely available. The principles taught are important for users of other programming languages, like C or C++.


The Statistical Analysis of Multivariate Failure Time Data

The Statistical Analysis of Multivariate Failure Time Data

Author: Ross L. Prentice

Publisher: CRC Press

Published: 2019-05-14

Total Pages: 110

ISBN-13: 0429529708

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The Statistical Analysis of Multivariate Failure Time Data: A Marginal Modeling Approach provides an innovative look at methods for the analysis of correlated failure times. The focus is on the use of marginal single and marginal double failure hazard rate estimators for the extraction of regression information. For example, in a context of randomized trial or cohort studies, the results go beyond that obtained by analyzing each failure time outcome in a univariate fashion. The book is addressed to researchers, practitioners, and graduate students, and can be used as a reference or as a graduate course text. Much of the literature on the analysis of censored correlated failure time data uses frailty or copula models to allow for residual dependencies among failure times, given covariates. In contrast, this book provides a detailed account of recently developed methods for the simultaneous estimation of marginal single and dual outcome hazard rate regression parameters, with emphasis on multiplicative (Cox) models. Illustrations are provided of the utility of these methods using Women’s Health Initiative randomized controlled trial data of menopausal hormones and of a low-fat dietary pattern intervention. As byproducts, these methods provide flexible semiparametric estimators of pairwise bivariate survivor functions at specified covariate histories, as well as semiparametric estimators of cross ratio and concordance functions given covariates. The presentation also describes how these innovative methods may extend to handle issues of dependent censorship, missing and mismeasured covariates, and joint modeling of failure times and covariates, setting the stage for additional theoretical and applied developments. This book extends and continues the style of the classic Statistical Analysis of Failure Time Data by Kalbfleisch and Prentice. Ross L. Prentice is Professor of Biostatistics at the Fred Hutchinson Cancer Research Center and University of Washington in Seattle, Washington. He is the recipient of COPSS Presidents and Fisher awards, the AACR Epidemiology/Prevention and Team Science awards, and is a member of the National Academy of Medicine. Shanshan Zhao is a Principal Investigator at the National Institute of Environmental Health Sciences in Research Triangle Park, North Carolina.


Statistical Analysis of Extreme Values

Statistical Analysis of Extreme Values

Author: Rolf-Dieter Reiss

Publisher: Springer Science & Business Media

Published: 2007-06-21

Total Pages: 516

ISBN-13: 3764372303

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This is a self-contained introduction to parametric modeling, exploratory analysis and statistical interference for extreme values, as used in disciplines from hydrology to finance to environmental science. Updated and expanded by 100 pages.


Research Design & Statistical Analysis

Research Design & Statistical Analysis

Author: Arnold D. Well

Publisher: Psychology Press

Published: 2003-01-30

Total Pages: 1013

ISBN-13: 1135641072

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This book emphasizes the statistical concepts and assumptions necessary to describe and make inferences about real data. Throughout the book the authors encourage the reader to plot and examine their data, find confidence intervals, use power analyses to determine sample size, and calculate effect sizes. The goal is to ensure the reader understands the underlying logic and assumptions of the analysis and what it tells them, the limitations of the analysis, and the possible consequences of violating assumptions. The simpler, less abstract discussion of analysis of variance is presented prior to developing the more general model. A concern for alternatives to standard analyses allows for the integration of non-parametric techniques into relevant design chapters, rather than in a single, isolated chapter. This organization allows for the comparison of the pros and cons of alternative procedures within the research context to which they apply. Basic concepts, such as sampling distributions, expected mean squares, design efficiency, and statistical models are emphasized throughout. This approach provides a stronger conceptual foundation in order to help the reader generalize the concepts to new situations they will encounter in their research and to better understand the advice of statistical consultants and the content of articles using statistical methodology. The second edition features a greater emphasis on graphics, confidence intervals, measures of effect size, power analysis, tests of contrasts, elementary probability, correlation, and regression. A Free CD that contains several real and artificial data sets used in the book in SPSS, SYSTAT, and ASCII formats, is included in the back of the book. An Instructor's Solutions Manual, containing the intermediate steps to all of the text exercises, is available free to adopters.


Functional and High-Dimensional Statistics and Related Fields

Functional and High-Dimensional Statistics and Related Fields

Author: Germán Aneiros

Publisher: Springer Nature

Published: 2020-06-19

Total Pages: 254

ISBN-13: 3030477568

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This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.


Statistical Analysis of Profile Monitoring

Statistical Analysis of Profile Monitoring

Author: Rassoul Noorossana

Publisher: John Wiley & Sons

Published: 2011-09-09

Total Pages: 298

ISBN-13: 1118071972

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A one-of-a-kind presentation of the major achievements in statistical profile monitoring methods Statistical profile monitoring is an area of statistical quality control that is growing in significance for researchers and practitioners, specifically because of its range of applicability across various service and manufacturing settings. Comprised of contributions from renowned academicians and practitioners in the field, Statistical Analysis of Profile Monitoring presents the latest state-of-the-art research on the use of control charts to monitor process and product quality profiles. The book presents comprehensive coverage of profile monitoring definitions, techniques, models, and application examples, particularly in various areas of engineering and statistics. The book begins with an introduction to the concept of profile monitoring and its applications in practice. Subsequent chapters explore the fundamental concepts, methods, and issues related to statistical profile monitoring, with topics of coverage including: Simple and multiple linear profiles Binary response profiles Parametric and nonparametric nonlinear profiles Multivariate linear profiles monitoring Statistical process control for geometric specifications Correlation and autocorrelation in profiles Nonparametric profile monitoring Throughout the book, more than two dozen real-world case studies highlight the discussed topics along with innovative examples and applications of profile monitoring. Statistical Analysis of Profile Monitoring is an excellent book for courses on statistical quality control at the graduate level. It also serves as a valuable reference for quality engineers, researchers and anyone who works in monitoring and improving statistical processes.


Illustrating Statistical Procedures: Finding Meaning in Quantitative Data

Illustrating Statistical Procedures: Finding Meaning in Quantitative Data

Author: Ray W. Cooksey

Publisher: Springer Nature

Published: 2020-05-14

Total Pages: 752

ISBN-13: 9811525374

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This book occupies a unique position in the field of statistical analysis in the behavioural and social sciences in that it targets learners who would benefit from learning more conceptually and less computationally about statistical procedures and the software packages that can be used to implement them. This book provides a comprehensive overview of this important research skill domain with an emphasis on visual support for learning and better understanding. The primary focus is on fundamental concepts, procedures and interpretations of statistical analyses within a single broad illustrative research context. The book covers a wide range of descriptive, correlational and inferential statistical procedures as well as more advanced procedures not typically covered in introductory and intermediate statistical texts. It is an ideal reference for postgraduate students as well as for researchers seeking to broaden their conceptual exposure to what is possible in statistical analysis.


Statistical Power Analysis for the Behavioral Sciences

Statistical Power Analysis for the Behavioral Sciences

Author: Jacob Cohen

Publisher: Routledge

Published: 2013-05-13

Total Pages: 625

ISBN-13: 1134742770

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Statistical Power Analysis is a nontechnical guide to power analysis in research planning that provides users of applied statistics with the tools they need for more effective analysis. The Second Edition includes: * a chapter covering power analysis in set correlation and multivariate methods; * a chapter considering effect size, psychometric reliability, and the efficacy of "qualifying" dependent variables and; * expanded power and sample size tables for multiple regression/correlation.


High-Dimensional Statistics

High-Dimensional Statistics

Author: Martin J. Wainwright

Publisher: Cambridge University Press

Published: 2019-02-21

Total Pages: 571

ISBN-13: 1108498027

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A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.


Statistical Analysis of High-dimensional Biomedical Data: a Gentle Introduction to Analytical Goals, Common Approaches and Challenges

Statistical Analysis of High-dimensional Biomedical Data: a Gentle Introduction to Analytical Goals, Common Approaches and Challenges

Author: Jörg Rahnenführer

Publisher:

Published: 2023

Total Pages: 0

ISBN-13:

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Abstract: Background In high-dimensional data (HDD) settings, the number of variables associated with each observation is very large. Prominent examples of HDD in biomedical research include omics data with a large number of variables such as many measurements across the genome, proteome, or metabolome, as well as electronic health records data that have large numbers of variables recorded for each patient. The statistical analysis of such data requires knowledge and experience, sometimes of complex methods adapted to the respective research questions. Methods Advances in statistical methodology and machine learning methods offer new opportunities for innovative analyses of HDD, but at the same time require a deeper understanding of some fundamental statistical concepts. Topic group TG9 "High-dimensional data" of the STRATOS (STRengthening Analytical Thinking for Observational Studies) initiative provides guidance for the analysis of observational studies, addressing particular statistical challenges and opportunities for the analysis of studies involving HDD. In this overview, we discuss key aspects of HDD analysis to provide a gentle introduction for non-statisticians and for classically trained statisticians with little experience specific to HDD. Results The paper is organized with respect to subtopics that are most relevant for the analysis of HDD, in particular initial data analysis, exploratory data analysis, multiple testing, and prediction. For each subtopic, main analytical goals in HDD settings are outlined. For each of these goals, basic explanations for some commonly used analysis methods are provided. Situations are identified where traditional statistical methods cannot, or should not, be used in the HDD setting, or where adequate analytic tools are still lacking. Many key references are provided. Conclusions This review aims to provide a solid statistical foundation for researchers, including statisticians and non-statisticians, who are new to research with HDD or simply want to better evaluate and understand the results of HDD analyses