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Author: Jennifer Lee Weeding
Publisher:
ISBN:
Category : Errors-in-variables models
Languages : en
Pages : 155
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Book Description
Measurement errors arise in a variety of circumstances and occur when a variable cannot be observed exactly, but instead is observed with error. For example, summary measures contain measurement error, as the true value of the variable is estimated from observed data that contain sampling variability. Measurement errors should be accounted for when they are present, as the impacts of ignoring measurement errors include bias in parameter estimates and a loss of power to detect effects. Measurement error models are used to account for measurement errors and correct parameter estimates for the bias induced from variables measured with error. To account for measurement errors when present, most correction methods require that the measurement error variance be known (or estimated). Common correction methods include the method of moments correction, the SIMEX correction, and Bayesian correction methods. The area under the curve (AUC) summary measure is commonly used in pharmaceutical studies to estimate the total concentration of a substance present in the blood over a given time interval. Other areas, such as Ecology, use the AUC to estimate the total count of a species present over a specified time interval. In situations where the AUC is estimated, a measure of the uncertainty associated with it is often desired. Due to the longitudinal nature of AUC data, the estimation of its variance is often not straightforward. In this research we develop a Bayesian method to estimate the variance of the AUC, where our focus is on accounting for the possible correlation structure between repeated observations on the same subject. This estimate can then be used in measurement error models to account for the measurement error induced from estimating the AUC. We study the performance of three measurement error correction methods in the simple linear regression setting, where measurement errors are present in the explanatory variable, the response variable, or both. We extend the Bayesian correction methods to account for uncorrelated and correlated measurement errors between variables. The methods were validated using both simulated and real data collected from an equine study of blood glucose measurements.
Author: Jennifer Lee Weeding
Publisher:
ISBN:
Category : Errors-in-variables models
Languages : en
Pages : 155
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Book Description
Measurement errors arise in a variety of circumstances and occur when a variable cannot be observed exactly, but instead is observed with error. For example, summary measures contain measurement error, as the true value of the variable is estimated from observed data that contain sampling variability. Measurement errors should be accounted for when they are present, as the impacts of ignoring measurement errors include bias in parameter estimates and a loss of power to detect effects. Measurement error models are used to account for measurement errors and correct parameter estimates for the bias induced from variables measured with error. To account for measurement errors when present, most correction methods require that the measurement error variance be known (or estimated). Common correction methods include the method of moments correction, the SIMEX correction, and Bayesian correction methods. The area under the curve (AUC) summary measure is commonly used in pharmaceutical studies to estimate the total concentration of a substance present in the blood over a given time interval. Other areas, such as Ecology, use the AUC to estimate the total count of a species present over a specified time interval. In situations where the AUC is estimated, a measure of the uncertainty associated with it is often desired. Due to the longitudinal nature of AUC data, the estimation of its variance is often not straightforward. In this research we develop a Bayesian method to estimate the variance of the AUC, where our focus is on accounting for the possible correlation structure between repeated observations on the same subject. This estimate can then be used in measurement error models to account for the measurement error induced from estimating the AUC. We study the performance of three measurement error correction methods in the simple linear regression setting, where measurement errors are present in the explanatory variable, the response variable, or both. We extend the Bayesian correction methods to account for uncorrelated and correlated measurement errors between variables. The methods were validated using both simulated and real data collected from an equine study of blood glucose measurements.
Author: Paul Gustafson
Publisher: CRC Press
ISBN: 1135441235
Category : Mathematics
Languages : en
Pages : 200
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Book Description
Mismeasurement of explanatory variables is a common hazard when using statistical modeling techniques, and particularly so in fields such as biostatistics and epidemiology where perceived risk factors cannot always be measured accurately. With this perspective and a focus on both continuous and categorical variables, Measurement Error and Misclassi
Author: Giulio D'agostini
Publisher: World Scientific
ISBN: 9814486094
Category : Mathematics
Languages : en
Pages : 351
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Book Description
This book provides a multi-level introduction to Bayesian reasoning (as opposed to “conventional statistics”) and its applications to data analysis. The basic ideas of this “new” approach to the quantification of uncertainty are presented using examples from research and everyday life. Applications covered include: parametric inference; combination of results; treatment of uncertainty due to systematic errors and background; comparison of hypotheses; unfolding of experimental distributions; upper/lower bounds in frontier-type measurements. Approximate methods for routine use are derived and are shown often to coincide — under well-defined assumptions! — with “standard” methods, which can therefore be seen as special cases of the more general Bayesian methods. In dealing with uncertainty in measurements, modern metrological ideas are utilized, including the ISO classification of uncertainty into type A and type B. These are shown to fit well into the Bayesian framework.
Author: Ming-Hui Chen
Publisher: Springer Science & Business Media
ISBN: 1441969446
Category : Mathematics
Languages : en
Pages : 631
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Book Description
Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.
Author: Jean-Paul Fox
Publisher:
ISBN:
Category :
Languages : en
Pages : 68
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Book Description
Author: Stephen Crowder
Publisher: Springer Nature
ISBN: 3030533298
Category : Mathematics
Languages : en
Pages : 357
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Book Description
This book provides an overview of the application of statistical methods to problems in metrology, with emphasis on modelling measurement processes and quantifying their associated uncertainties. It covers everything from fundamentals to more advanced special topics, each illustrated with case studies from the authors' work in the Nuclear Security Enterprise (NSE). The material provides readers with a solid understanding of how to apply the techniques to metrology studies in a wide variety of contexts. The volume offers particular attention to uncertainty in decision making, design of experiments (DOEx) and curve fitting, along with special topics such as statistical process control (SPC), assessment of binary measurement systems, and new results on sample size selection in metrology studies. The methodologies presented are supported with R script when appropriate, and the code has been made available for readers to use in their own applications. Designed to promote collaboration between statistics and metrology, this book will be of use to practitioners of metrology as well as students and researchers in statistics and engineering disciplines.
Author: Xiaofeng Wang
Publisher: CRC Press
ISBN: 1351165755
Category : Mathematics
Languages : en
Pages : 312
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Book Description
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.
Author: Andrew Gelman
Publisher: CRC Press
ISBN: 1439840954
Category : Mathematics
Languages : en
Pages : 677
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Book Description
Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Author: Samuel A. Schmitt
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 424
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Book Description
Author: John P. Buonaccorsi
Publisher: CRC Press
ISBN: 1420066587
Category : Mathematics
Languages : en
Pages : 465
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Book Description
Over the last 20 years, comprehensive strategies for treating measurement error in complex models and accounting for the use of extra data to estimate measurement error parameters have emerged. Focusing on both established and novel approaches, Measurement Error: Models, Methods, and Applications provides an overview of the main techniques and illu
