Download or read book Bayesian Approaches to Parameter Estimation and Variable Selection for Misclassified Binary Data written by Daniel Beavers and published by . This book was released on 2009 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Binary misclassification is a common occurrence in statistical studies that, when ignored, induces bias in parameter estimates. The development of statistical methods to adjust for misclassification is necessary to allow for consistent estimation of parameters. In this work we develop a Bayesian framework for adjusting statistical models when fallible data collection methods produce misclassification of binary observations. In Chapter 2, we develop an approach for Bayesian variable selection for logistic regression models in which there exists a misclassified binary covariate. In this case, we require a subsample of gold standard validation data to estimate the sensitivity and specificity of the fallible classifier. In Chapter 3, we propose a Bayesian approach for the estimation of population prevalence of a biomarker in repeated diagnostic testing studies. In such situations, it is necessary to account for interindividual variability which we achieve through both the inclusion of random effects within logistic regression models and Bayesian hierarchical modeling. Our examples focus on applications for both reliability studies and biostatistical studies. Finally, we develop an approach to attempt to detect conditional dependence parameters between two fallible diagnostic tests for a binary logistic regression covariate in the absence of a gold standard test in Chapter 4. We compare the performance of the proposed procedure to previously published means assessing model fit.

Download or read book Bayesian Approach to Inference and Variable Selection for Misclassified and Under reported Response Models written by Stephanie L. Powers and published by . This book was released on 2009 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Response partial missingness is a problem in studies conducted in a variety of disciplines. We investigate the impact ignoring response partial missingness has on determining a subset of significant covariates in non-linear regression. In particular, we consider non-differential misclassification in logistic regression and non-differential under-reporting in Poisson regression. Differential misclassification and differential under-reporting are also addressed but in less detail. We then develop a Bayesian approach to select significant covariates while accounting for the partial missingness. Examples of response partial missingness in which the variable selection method is applied include determining the factors that contribute to whether or not an individual will stop smoking and how many days an individual is absent from work.

Download or read book Handbook of Bayesian Variable Selection written by Mahlet G. Tadesse and published by CRC Press. This book was released on 2021-12-24 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material

Download or read book Essays on Bayesian Time Series and Variable Selection written by Debkumar De and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimating model parameters in dynamic model continues to be challenge. In my dissertation, we have introduced a Stochastic Approximation based parameter estimation approach under Ensemble Kalman Filter set-up. Asymptotic properties of the resultant estimates are discussed here. We have compared our proposed method to current methods via simulation studies. We have demonstrated predictive performance of our proposed method on a large spatio-temporal data. In my other topic, we presented a method for simultaneous estimation of regression parameters and the covariance matrix, developed for a nonparametric Seemingly Unrelated Regression problem. This is a very flexible modeling technique that essentially performs a sparse high-dimensional multiple predictor(p), multiple responses(q) regression where the responses may be correlated. Such data appear abundantly in the fields of genomics, finance and econometrics. We illustrate and compare performances of our proposed techniques with previous analyses using both simulated and real multivariate data arising in econometrics and government. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/152793

Download or read book Bayesian Parameter Estimation and Variable Selection for Quantile Regression written by Craig Reed and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Determining Bayesian Sample Size and Bayesian Optimal Model written by Dunlei Cheng and published by LAP Lambert Academic Publishing. This book was released on 2010-01 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation contains three topics using the Bayesian paradigm for statistical inference. The first topic is related to Bayesian sample size determination with a misclassified prevalence variable when two possibly dependent diagnostic tests are used for estimation. After accounting for the dependence structure, the required sample size will be larger than that assuming independence between the tests. The second topic is also concerned with Bayesian sample size calculation with a misclassified binary response variable. Differing from the first topic, an error-free covariate is added. Simulations demonstrate that choices of prior distributions have a great impact on the resultant sample size. The last topic is about Bayesian variable selection under the multiple linear regression model. Two competing Bayesian methods are Bayesian model averaging and reversible jump MCMC. It is found that reversible jump MCMC, expected to give better models, does not seem to differ from Bayesian model averaging in examples considered.

Download or read book Frontiers of Statistical Decision Making and Bayesian Analysis written by Ming-Hui Chen and published by Springer Science & Business Media. This book was released on 2010-07-24 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Bayesian Inference written by Hanns L. Harney and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving a longstanding problem in the physical sciences, this text and reference generalizes Gaussian error intervals to situations in which the data follow distributions other than Gaussian. The text is written at introductory level, with many examples and exercises.

Download or read book Adjustment Uncertainty and Variable Selection in a Bayesian Context written by Andrew James Dennis Henrey and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Model Averaging (BMA) has previously been proposed as a solution to the variable selection problem when there is uncertainty about the true model in regression. Some recent research discusses the drawbacks; specifically, BMA can (and does) give biased parameter estimates in the presence of confounding. This is because BMA is optimized for prediction rather than parameter estimation. Though some newer research attempts to fix the issue of bias under confounding, none of the current algorithms handle either large data sets or survival outcomes. The Approximate Two-phase Bayesian Adjustment for Confounding (ATBAC) algorithm proposed in this paper does both, and we use it on a large medical cohort study called THIN (The Health Improvement Network) to estimate the effect of statins on risk of stroke. We use simulation and some analytical techniques to discuss two main topics in this paper. Firstly, we demonstrate the ability of ATBAC to perform unbiased parameter estimation on survival data while accounting for model uncertainty. Secondly, we discuss when it is, and isn't, helpful to use variable selection techniques in the first place, and find that in some large data sets variable selection for parameter estimation is unnecessary.

Download or read book A Comparison of the Bayesian and Frequentist Approaches to Estimation written by Francisco J. Samaniego and published by Springer Science & Business Media. This book was released on 2010-06-14 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this monograph is “comparative statistical inference. ” While the topics covered have been carefully selected (they are, for example, restricted to pr- lems of statistical estimation), my aim is to provide ideas and examples which will assist a statistician, or a statistical practitioner, in comparing the performance one can expect from using either Bayesian or classical (aka, frequentist) solutions in - timation problems. Before investing the hours it will take to read this monograph, one might well want to know what sets it apart from other treatises on comparative inference. The two books that are closest to the present work are the well-known tomes by Barnett (1999) and Cox (2006). These books do indeed consider the c- ceptual and methodological differences between Bayesian and frequentist methods. What is largely absent from them, however, are answers to the question: “which - proach should one use in a given problem?” It is this latter issue that this monograph is intended to investigate. There are many books on Bayesian inference, including, for example, the widely used texts by Carlin and Louis (2008) and Gelman, Carlin, Stern and Rubin (2004). These books differ from the present work in that they begin with the premise that a Bayesian treatment is called for and then provide guidance on how a Bayesian an- ysis should be executed. Similarly, there are many books written from a classical perspective.

Download or read book Bayesian Variable Selection and Estimation written by Xiaofan Xu and published by . This book was released on 2014 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper considers the classical Bayesian variable selection problem and an important subproblem in which grouping information of predictors is available. We propose the Half Thresholding (HT) estimator for simultaneous variable selection and estimation with shrinkage priors. Under orthogonal design matrix, variable selection consistency and asymptotic distribution of HT estimators are investigated and the oracle property is established with Three Parameter Beta Mixture of Normals (TPBN) priors. We then revisit Bayesian group lasso and use spike and slab priors for variable selection at the group level. In the process, the connection of our model with penalized regression is demonstrated, and the role of posterior median for thresholding is pointed out. We show that the posterior median estimator has the oracle property for group variable selection and estimation under orthogonal design while the group lasso has suboptimal asymptotic estimation rate when variable selection consistency is achieved. Next we consider Bayesian sparse group lasso again with spike and slab priors to select variables both at the group level and also within the group, and develop the necessary algorithm for its implementation. We demonstrate via simulation that the posterior median estimator of our spike and slab models has excellent performance for both variable selection and estimation.

Download or read book Advances In Statistics Combinatorics And Related Areas Selected Papers From The Scra2001 fim Viii Procs Of The Wollongong Conference written by Chandra Gulati and published by World Scientific. This book was released on 2002-12-19 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of selected refereed papers presented at the International Conference on Statistics, Combinatorics and Related Areas, and the Eighth International Conference of the Forum for Interdisciplinary Mathematics. It includes contributions from eminent statisticians such as Joe Gani, Clive Granger, Chris Heyde, R Nishii, C R Rao, P K Sen and Sue Wilson. By exploring and investigating deeper, these papers enlarge the reservoir in the represented areas of research, such as bioinformatics, estimating functions, financial statistics, generalized linear models, goodness of fit, image analysis, industrial data analysis, multivariate statistics, neural networks, quasi-likelihood, sample surveys, statistical inference, stochastic models, and time series.

Download or read book Introduction to Bayesian Estimation and Copula Models of Dependence written by Arkady Shemyakin and published by John Wiley & Sons. This book was released on 2017-03-03 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to Bayesian statistics, presents an emphasis on Bayesian methods (prior and posterior), Bayes estimation, prediction, MCMC,Bayesian regression, and Bayesian analysis of statistical modelsof dependence, and features a focus on copulas for risk management Introduction to Bayesian Estimation and Copula Models of Dependence emphasizes the applications of Bayesian analysis to copula modeling and equips readers with the tools needed to implement the procedures of Bayesian estimation in copula models of dependence. This book is structured in two parts: the first four chapters serve as a general introduction to Bayesian statistics with a clear emphasis on parametric estimation and the following four chapters stress statistical models of dependence with a focus of copulas. A review of the main concepts is discussed along with the basics of Bayesian statistics including prior information and experimental data, prior and posterior distributions, with an emphasis on Bayesian parametric estimation. The basic mathematical background of both Markov chains and Monte Carlo integration and simulation is also provided. The authors discuss statistical models of dependence with a focus on copulas and present a brief survey of pre-copula dependence models. The main definitions and notations of copula models are summarized followed by discussions of real-world cases that address particular risk management problems. In addition, this book includes: • Practical examples of copulas in use including within the Basel Accord II documents that regulate the world banking system as well as examples of Bayesian methods within current FDA recommendations • Step-by-step procedures of multivariate data analysis and copula modeling, allowing readers to gain insight for their own applied research and studies • Separate reference lists within each chapter and end-of-the-chapter exercises within Chapters 2 through 8 • A companion website containing appendices: data files and demo files in Microsoft® Office Excel®, basic code in R, and selected exercise solutions Introduction to Bayesian Estimation and Copula Models of Dependence is a reference and resource for statisticians who need to learn formal Bayesian analysis as well as professionals within analytical and risk management departments of banks and insurance companies who are involved in quantitative analysis and forecasting. This book can also be used as a textbook for upper-undergraduate and graduate-level courses in Bayesian statistics and analysis. ARKADY SHEMYAKIN, PhD, is Professor in the Department of Mathematics and Director of the Statistics Program at the University of St. Thomas. A member of the American Statistical Association and the International Society for Bayesian Analysis, Dr. Shemyakin's research interests include informationtheory, Bayesian methods of parametric estimation, and copula models in actuarial mathematics, finance, and engineering. ALEXANDER KNIAZEV, PhD, is Associate Professor and Head of the Department of Mathematics at Astrakhan State University in Russia. Dr. Kniazev's research interests include representation theory of Lie algebras and finite groups, mathematical statistics, econometrics, and financial mathematics.

Download or read book Bayesian Inference on Complicated Data written by Niansheng Tang and published by BoD – Books on Demand. This book was released on 2020-07-15 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to great applications in various fields, such as social science, biomedicine, genomics, and signal processing, and the improvement of computing ability, Bayesian inference has made substantial developments for analyzing complicated data. This book introduces key ideas of Bayesian sampling methods, Bayesian estimation, and selection of the prior. It is structured around topics on the impact of the choice of the prior on Bayesian statistics, some advances on Bayesian sampling methods, and Bayesian inference for complicated data including breast cancer data, cloud-based healthcare data, gene network data, and longitudinal data. This volume is designed for statisticians, engineers, doctors, and machine learning researchers.

Download or read book A Bayesian Variable Selection Method with Applications to Spatial Data written by Xiahan Tang and published by . This book was released on 2017 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis first describes the general idea behind Bayes Inference, various sampling methods based on Bayes theorem and many examples. Then a Bayes approach to model selection, called Stochastic Search Variable Selection (SSVS) is discussed. It was originally proposed by George and McCulloch (1993). In a normal regression model where the number of covariates is large, only a small subset tend to be significant most of the times. This Bayes procedure specifies a mixture prior for each of the unknown regression coefficient, the mixture prior was originally proposed by Geweke (1996). This mixture prior will be updated as data becomes available to generate a posterior distribution that assigns higher posterior probabilities to coefficients that are significant in explaining the response. Spatial modeling method is described in this thesis. Prior distribution for all unknown parameters and latent variables are specified. Simulated studies under different models have been implemented to test the efficiency of SSVS. A real dataset taken by choosing a small region from the Cape Floristic Region in South Africa is used to analyze the plants distribution in that region. The original multi-cateogory response is transformed into a presence and absence (binary) response for simpler analysis. First, SSVS is used on this dataset to select the subset of significant covariates. Then a spatial model is fitted using the chosen covariates and, post-estimation, predictive map of posterior probabilities of presence and absence are obtained for the study region. Posterior estimates for the true regression coefficients are also provided along with map for spatial random effects.

Download or read book Bayesian Methods written by Thomas Leonard and published by Cambridge University Press. This book was released on 2001-08-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian statistics directed towards mainstream statistics. How to infer scientific, medical, and social conclusions from numerical data.

Download or read book Bayesian Methods for Data Analysis Third Edition written by Bradley P. Carlin and published by CRC Press. This book was released on 2008-06-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broadening its scope to nonstatisticians, Bayesian Methods for Data Analysis, Third Edition provides an accessible introduction to the foundations and applications of Bayesian analysis. Along with a complete reorganization of the material, this edition concentrates more on hierarchical Bayesian modeling as implemented via Markov chain Monte Carlo (MCMC) methods and related data analytic techniques. New to the Third Edition New data examples, corresponding R and WinBUGS code, and homework problems Explicit descriptions and illustrations of hierarchical modeling—now commonplace in Bayesian data analysis A new chapter on Bayesian design that emphasizes Bayesian clinical trials A completely revised and expanded section on ranking and histogram estimation A new case study on infectious disease modeling and the 1918 flu epidemic A solutions manual for qualifying instructors that contains solutions, computer code, and associated output for every homework problem—available both electronically and in print Ideal for Anyone Performing Statistical Analyses Focusing on applications from biostatistics, epidemiology, and medicine, this text builds on the popularity of its predecessors by making it suitable for even more practitioners and students.