Convergence Rates For Empirical Bayes Two Action Problems Ii Continuous Case PDF Download

Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Convergence Rates For Empirical Bayes Two Action Problems Ii Continuous Case PDF full book. Access full book title Convergence Rates For Empirical Bayes Two Action Problems Ii Continuous Case.

Convergence Rates for Empirical Bayes Two-action Problems II, Continuous Case

Convergence Rates for Empirical Bayes Two-action Problems II, Continuous Case
Author: STANFORD UNIV CALIF DEPT OF STATISTICS.
Publisher:
Total Pages: 28
Release: 1967
Genre:
ISBN:
GET BOOK

Download Convergence Rates for Empirical Bayes Two-action Problems II, Continuous Case Book in PDF, ePub and Kindle

A sequence of decision problems is considered where for each problem the observation has a probability density function of exponential type with parameter lambda where lambda is selected independently for each problem according to an unknown prior distribution G(lambda). It is supposed that in each of the problems, one of two possible actions (e.g., 'accept' or 'reject') must be taken. Under various assumptions, reasonably sharp upper bounds are found for the rate at which the risk of the nth problem approaches the smallest possible risk for certain refinements of the standard empirical Bayes procedures. For suitably chosen procedures, under situations likely to occur in practice, rates faster than n to the power ( -1 + epsilon) may be obtained for arbitrarily small epsilon> 0. Arbitrarily slow rates can occur in pathological situations. (Author).

Convergence Rates for Empirical Bayes Two-action Problems I. Discrete Case

Convergence Rates for Empirical Bayes Two-action Problems I. Discrete Case
Author: STANFORD UNIV CALIF DEPT OF STATISTICS.
Publisher:
Total Pages: 41
Release: 1967
Genre:
ISBN:
GET BOOK

Download Convergence Rates for Empirical Bayes Two-action Problems I. Discrete Case Book in PDF, ePub and Kindle

A sequence of decision problems is considered where for each problem the observation has discrete probability function of the form p(x) = h(x) beta (lambda) lambda to the power x, x = 0,1,2, ..., and where lambda is selected independently for each problem according to an unknown prior distribution G(lambda). It is supposed that for each problem one of two possible actions (e.g., 'accept' or 'reject') must be selected. Under various assumptions about h(x) and G(lambda) the rate at which the risk of the nth problem approaches the smallest possible risk is determined for standard empirical Bayes procedures. It is shown that for most practical situations, the rate of convergence to 'optimality' will be at least as fast as L(n)/n where L(n) is a slowly varying function (e.g., log n). The rate cannot be faster than 1/n and this exact rate is achieved in some cases. Arbitrarily slow rates will occur in certain pathological situations. (Author).

On the Convergence Rates of Empirical Bayes Rules for Two-Action Problems. Discrete Case

On the Convergence Rates of Empirical Bayes Rules for Two-Action Problems. Discrete Case
Author: Ta Chen Liang
Publisher:
Total Pages: 16
Release: 1987
Genre:
ISBN:
GET BOOK

Download On the Convergence Rates of Empirical Bayes Rules for Two-Action Problems. Discrete Case Book in PDF, ePub and Kindle

The purpose of this paper is to investigate the convergence rates of a sequence of empirical Bayes decision rules for the two-action decision problems where the distributions of the observations belong to a discrete exponential family. It is found that the sequence of the empirical Bayes decision rules under study is asymptotically optimal, and the order of associated convergence rates is O(exp( -cn)), for some positive constant c, where n is the number of accumulated past experience (observations) at hand. Two examples are provided to illustrate the performance of the proposed empirical Bayes decision rules. A comparison is also made between the proposed empirical Bayes rules and some earlier existng empirical Bayes rules.

Empirical Bayes and Likelihood Inference

Empirical Bayes and Likelihood Inference
Author: S.E. Ahmed
Publisher: Springer Science & Business Media
Total Pages: 242
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461301416
GET BOOK

Download Empirical Bayes and Likelihood Inference Book in PDF, ePub and Kindle

Bayesian and such approaches to inference have a number of points of close contact, especially from an asymptotic point of view. Both emphasize the construction of interval estimates of unknown parameters. In this volume, researchers present recent work on several aspects of Bayesian, likelihood and empirical Bayes methods, presented at a workshop held in Montreal, Canada. The goal of the workshop was to explore the linkages among the methods, and to suggest new directions for research in the theory of inference.

A Mixture Model Approach to Empirical Bayes Testing and Estimation

A Mixture Model Approach to Empirical Bayes Testing and Estimation
Author: Omkar Muralidharan
Publisher: Stanford University
Total Pages: 89
Release: 2011
Genre:
ISBN:
GET BOOK

Download A Mixture Model Approach to Empirical Bayes Testing and Estimation Book in PDF, ePub and Kindle

Many modern statistical problems require making similar decisions or estimates for many different entities. For example, we may ask whether each of 10,000 genes is associated with some disease, or try to measure the degree to which each is associated with the disease. As in this example, the entities can often be divided into a vast majority of "null" objects and a small minority of interesting ones. Empirical Bayes is a useful technique for such situations, but finding the right empirical Bayes method for each problem can be difficult. Mixture models, however, provide an easy and effective way to apply empirical Bayes. This thesis motivates mixture models by analyzing a simple high-dimensional problem, and shows their practical use by applying them to detecting single nucleotide polymorphisms.

Selected Papers

Selected Papers
Author: Herbert Robbins
Publisher: Springer
Total Pages: 530
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461251109
GET BOOK

Download Selected Papers Book in PDF, ePub and Kindle

Herbert Robbins is widely recognized as one of the most creative and original mathematical statisticians of our time. The purpose of this book is to reprint, on the occasion of his seventieth birthday, some of his most outstanding research. In making selections for reprinting we have tried to keep in mind three potential audiences: (1) the historian who would like to know Robbins' seminal role in stimulating a substantial proportion of current research in mathematical statistics; (2) the novice who would like a readable, conceptually oriented introduction to these subjects; and (3) the expert who would like to have useful reference material in a single collection. In many cases the needs of the first two groups can be met simulta neously. A distinguishing feature of Robbins' research is its daring originality, which literally creates new specialties for subsequent generations of statisticians to explore. Often these seminal papers are also models of exposition serving to introduce the reader, in the simplest possible context, to ideas that are important for contemporary research in the field. An example is the paper of Robbins and Monro which initiated the subject of stochastic approximation. We have also attempted to provide some useful guidance to the literature in various subjects by supplying additional references, particularly to books and survey articles, with some remarks about important developments in these areas.