Download or read book Revisiting Empirical Bayes Methods and Applications to Special Types of Data written by Xiuwen Duan and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical Bayes methods have been around for a long time and have a wide range of applications. These methods provide a way in which historical data can be aggregated to provide estimates of the posterior mean. This thesis revisits some of the empirical Bayesian methods and develops new applications. We first look at a linear empirical Bayes estimator and apply it on ranking and symbolic data. Next, we consider Tweedie's formula and show how it can be applied to analyze a microarray dataset. The application of the formula is simplified with the Pearson system of distributions. Saddlepoint approximations enable us to generalize several results in this direction. The results show that the proposed methods perform well in applications to real data sets.
Download or read book Empirical Bayes Methods with Applications written by J.S. Maritz and published by CRC Press. This book was released on 2018-01-18 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of Empirical Bayes Methods details are provided of the derivation and the performance of empirical Bayes rules for a variety of special models. Attention is given to the problem of assessing the goodness of an empirical Bayes estimator for a given set of prior data. A chapter is devoted to a discussion of alternatives to the empirical Bayes approach and there is also a chapter giving details of several actual applications of empirical Bayes method.
Download or read book Empirical Bayes Methods written by J. S. Maritz and published by . This book was released on 1970 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Large Scale Inference written by Bradley Efron and published by Cambridge University Press. This book was released on 2012-11-29 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples.
Download or read book Bayes and Empirical Bayes Methods for Data Analysis written by Bradley P. Carlin and published by . This book was released on 1996 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Bayes and Empirical Bayes Methods for Data Analysis Second Edition written by Bradley P. Carlin and published by Chapman and Hall/CRC. This book was released on 2000-06-22 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, Bayes and empirical Bayes (EB) methods have continued to increase in popularity and impact. Building on the first edition of their popular text, Carlin and Louis introduce these methods, demonstrate their usefulness in challenging applied settings, and show how they can be implemented using modern Markov chain Monte Carlo (MCMC) methods. Their presentation is accessible to those new to Bayes and empirical Bayes methods, while providing in-depth coverage valuable to seasoned practitioners. With its broad appeal as a text for those in biomedical science, education, social science, agriculture, and engineering, this second edition offers a relatively gentle and comprehensive introduction for students and practitioners already familiar with more traditional frequentist statistical methods. Focusing on practical tools for data analysis, the book shows how properly structured Bayes and EB procedures typically have good frequentist and Bayesian performance, both in theory and in practice.
Download or read book Statistical Rethinking written by Richard McElreath and published by CRC Press. This book was released on 2018-01-03 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.
Download or read book Empirical Bayes methods for spatial data written by Hubert Kostal and published by . This book was released on 1985 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonparametric Perspectives on Empirical Bayes written by Nikolaos Ignatiadis and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of when and why empirical Bayes point estimates accurately recover oracle Bayes behavior--in particular when the likelihood of the individual statistical problems is known and all problems are relevant to each other. In this thesis, we build upon advances in the theory of nonparametric statistics, machine learning, and computation to make three-fold contributions to the empirical Bayes literature: 1) We develop flexible and practical confidence intervals that provide asymptotic frequentist coverage of empirical Bayes estimands, such as the posterior mean or the local false sign rate. The coverage statements hold even when the estimands are only partially identified or when empirical Bayes point estimates converge very slowly. 2) We show that it is possible to achieve near-Bayes optimal mean squared error for the estimation of n effect sizes in the setting where both the prior and the per-problem likelihood are unknown. The requirement of our method is that we have access to replicated data, that is, each effect size of interest is estimated from K> 1 noisy observations. 3) We tackle the issue of relevance in empirical Bayes estimation of effect sizes. We propose a method that shrinks toward a per-problem location determined by a machine learning model prediction of the effect given side-information. We establish an extension to the classic result of James-Stein, whereby our proposed estimator dominates the sample mean for each problem under quadratic risk; even if the side-information contains no information about the true effects, or the machine learning model is arbitrarily miscalibrated. Taken together, these results broaden the applicability of empirical Bayes methods in areas such as genomics, and large scale experimentation, and demonstrate that it is fruitful to revisit traditional ideas in the empirical Bayes literature through a modern lens. The above results largely draw upon the following papers: Ignatiadis and Wager (2019, 2022) and Ignatiadis, Saha, Sun, and Muralidharan (2021).
Download or read book Generalized Empirical Bayes written by Douglas Fletcher and published by . This book was released on 2019 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two key issues of modern Bayesian statistics are: (i) establishing a principled approach for \textit{distilling} a statistical prior distribution that is \textit{consistent} with the given data from an initial believable scientific prior; and (ii) development of a \textit{consolidated} Bayes-frequentist data analysis workflow that is more effective than either of the two separately. In this thesis, we propose generalized empirical Bayes as a new framework for exploring these fundamental questions along with a wide range of applications spanning fields as diverse as clinical trials, metrology, insurance, medicine, and ecology. Our research marks a significant step towards bridging the ``gap'' between Bayesian and frequentist schools of thought that has plagued statisticians for over 250 years. Chapters 1 and 2--based on \cite{mukhopadhyay2018generalized}--introduces the core theory and methods of our proposed generalized empirical Bayes (gEB) framework that solves a long-standing puzzle of modern Bayes, originally posed by Herbert Robbins (1980). One of the main contributions of this research is to introduce and study a new class of nonparametric priors ${\rm DS}(G, m)$ that allows exploratory Bayesian modeling. However, at a practical level, major practical advantages of our proposal are: (i) computational ease (it does not require Markov chain Monte Carlo (MCMC), variational methods, or any other sophisticated computational techniques); (ii) simplicity and interpretability of the underlying theoretical framework which is general enough to include almost all commonly encountered models; and (iii) easy integration with mainframe Bayesian analysis that makes it readily applicable to a wide range of problems. Connections with other Bayesian cultures are also presented in the chapter. Chapter 3 deals with the topic of measurement uncertainty from a new angle by introducing the foundation of nonparametric meta-analysis. We have applied the proposed methodology to real data examples from astronomy, physics, and medical disciplines. Chapter 4 discusses some further extensions and application of our theory to distributed big data modeling and the missing species problem. The dissertation concludes by highlighting two important areas of future work: a full Bayesian implementation workflow and potential applications in cybersecurity.
Download or read book Bayesian Data Analysis Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Empirical Bayes Methods Applied to Spatial Analysis Problems written by Rand Corporation and published by . This book was released on 1970 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Empirical Bayes Methods in Time Series Analysis written by Taghi M. Khoshgoftaar and published by . This book was released on 1982 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Connecticut River Ecological Study 1965 1973 Revisited written by Paul M. Jacobson and published by . This book was released on 2004 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Revisiting Targeting in Social Assistance written by Margaret Grosh and published by World Bank Publications. This book was released on 2022-06-14 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Targeting is a commonly used, but much debated, policy tool within global social assistance practice. Revisiting Targeting in Social Assistance: A New Look at Old Dilemmas examines the well-known dilemmas in light of the growing body of experience, new implementation capacities, and the potential to bring new data and data science to bear. The book begins by considering why or whether or how narrowly or broadly to target different parts of social assistance and updates the global empirics around the outcomes and costs of targeting. It illustrates the choices that must be made in moving from an abstract vision to implementable definitions and procedures, and in deciding how the choices should be informed by values, empirics, and context. The importance of delivery systems and processes to distributional outcomes are emphasized, and many facets with room for improvement are discussed. The book also explores the choices between targeting methods and how differences in purposes and contexts shape those. The know-how with respect to the data and inference used by the different household-specific targeting methods is summarized and comprehensively updated, including a focus on “big data†? and machine learning. A primer on measurement issues is included. Key findings include the following: · Targeting selected categories, families, or individuals plays a valuable role within the framework of universal social protection. · Measuring the accuracy and cost of targeting can be done in many ways, and judicious choices require a range of metrics. · Weighing the relatively low costs of targeting against the potential gains is important. · Implementing inclusive delivery systems is critical for reducing errors of exclusion and inclusion. · Selecting and customizing the appropriate targeting method depends on purpose and context; there is no method preferred in all circumstances. · Leveraging advances in technology—ICT, big data, artificial intelligence, machine learning—can improve targeting accuracy, but they are not a panacea; better data matters more than sophistication in inference. · Targeting social protection should be a dynamic process.
Download or read book Data Gathering Analysis and Protection of Privacy Through Randomized Response Techniques Qualitative and Quantitative Human Traits written by and published by Elsevier. This book was released on 2016-04-20 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data Gathering, Analysis and Protection of Privacy through Randomized Response Techniques: Qualitative and Quantitative Human Traits tackles how to gather and analyze data relating to stigmatizing human traits. S.L. Warner invented RRT and published it in JASA, 1965. In the 50 years since, the subject has grown tremendously, with continued growth. This book comprehensively consolidates the literature to commemorate the inception of RR. Brings together all relevant aspects of randomized response and indirect questioning Tackles how to gather and analyze data relating to stigmatizing human traits Gives an encyclopedic coverage of the topic Covers recent developments and extrapolates to future trends
