Empirical Bayes Methods With Applications

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Empirical Bayes Methods With Applications

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Author : J.S. Maritz
language : en
Publisher: CRC Press
Release Date : 2018-01-18

Empirical Bayes Methods With Applications written by J.S. Maritz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.

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.

Empirical Bayes Methods

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Author : J. S. Maritz
language : en
Publisher:
Release Date : 1970

Empirical Bayes Methods written by J. S. Maritz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.

Revisiting Empirical Bayes Methods And Applications To Special Types Of Data

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Author : Xiuwen Duan
language : en
Publisher:
Release Date : 2021

Revisiting Empirical Bayes Methods And Applications To Special Types Of Data written by Xiuwen Duan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

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.

Empirical Bayes Methods With Applications

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Author : J.S. Maritz
language : en
Publisher: CRC Press
Release Date : 2018-01-18

Empirical Bayes Methods With Applications written by J.S. Maritz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.

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.

Large Scale Inference

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Author : Bradley Efron
language : en
Publisher: Cambridge University Press
Release Date : 2012-11-29

Large Scale Inference written by Bradley Efron and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-29 with Mathematics categories.

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.

Bayesian Theory And Methods With Applications

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Author : Vladimir Savchuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-01

Bayesian Theory And Methods With Applications written by Vladimir Savchuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-01 with Mathematics categories.

Bayesian methods are growing more and more popular, finding new practical applications in the fields of health sciences, engineering, environmental sciences, business and economics and social sciences, among others. This book explores the use of Bayesian analysis in the statistical estimation of the unknown phenomenon of interest. The contents demonstrate that where such methods are applicable, they offer the best possible estimate of the unknown. Beyond presenting Bayesian theory and methods of analysis, the text is illustrated with a variety of applications to real world problems.

Statistical Estimation By The Empirical Bayes Method Some Extensions And Logistical Applications

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Author : S. James Press
language : en
Publisher:
Release Date : 1965

Statistical Estimation By The Empirical Bayes Method Some Extensions And Logistical Applications written by S. James Press and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Logistics categories.

This report contains a presentation of the empirical Bayes procedure for improving existing methods of estimating statistical decision parameters which occur in such logistical problems as reliability, maintenance, and supply. It consists essentially of estimating a parameter by using an approximate Bayes estimator that does not depend on any previous information, other than earlier observations. The author presents estimators for the univariate and multivariate exponential family of distributions, for distributions with nuisance parameters, and for the distribution of a family of random variables (Poisson process). (Author).

The Utility Of Empirical Bayes Methods For Comparing Regression Structures In Small Subsamples

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Author : Ross M. Stolzenberg
language : en
Publisher:
Release Date : 1987

The Utility Of Empirical Bayes Methods For Comparing Regression Structures In Small Subsamples written by Ross M. Stolzenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Regression analysis categories.

Generalized Empirical Bayes

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Author : Douglas Fletcher
language : en
Publisher:
Release Date : 2019

Generalized Empirical Bayes written by Douglas Fletcher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

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.

Application Of The Empirical Bayes Method In A Comparative Microarray Experiment

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Author : Ying Wang
language : en
Publisher:
Release Date : 2002

Application Of The Empirical Bayes Method In A Comparative Microarray Experiment written by Ying Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Bayesian statistical decision theory categories.