Incorporating historical controls using a random-effects model with a normal prior

Employing a variance stabilization transformation, a random-effects model with a normal prior is proposed for incorporating historical controls in the estimation of dose-response relationships. The advantages and disadvantages of maximum likelihood and empirical Bayes estimators are discussed. A two-stage method is introduced for the prudent use of historical controls.     

Estimation in noncentral distributions

This paper investigates alternatives to MIU estimators in noncentral X ² and F distributions. Two directions are pursued. In the first, a general approach for uniformly improving on MVU estimators is described and illustrated. In the second, Bayesian, procedures are characterized and illustrated as well. This effort extends earlier work of Perlman and Rasmussen and of Neff and Strawderman.     

Confidence sets and the stein effect

The problem of improving upon the usual set estimator of a multivariate normal mean has only recently seen significant advances. Improved sets that take advantage of the Stein effect have been constructed. It is shown here that the Stein effect is so powerful that one can construct improved confidence sets that can have zero radius on a set of positive probability. Other, somewhat more sensible, sets which attain arbitrarily small radius are also constructed, and it is argued that one way to eliminate unreasonable confidence sets is through a conditional evaluation.     

Admissible estimation in an one parameter nonregular family of absolutely continuous distributions

Consider the problem of estimating under squared error loss an arbitrarily positive, strictly increasing or decreasing parametric function based on a sample of size n in an one parameter nonregular family of absolutly continuous distributions with both endpoints of the support depending on a single parameter. We first provide sufficient conditions for the admissibility of generalized Bayes estimators with respect to some specific priors and then treat several examples which illustrate the admissibility of best invariant estimators in some location or scale parameter problems.     

Estimation of random coefficient regression models

Linear regression models with coefficients across individual units regarded as random samples from some population are studied in this article from a Bayesian viewpoint. A prior distribution of the secondary parameters is derived following the Jeffreys rule. Posterior distribution of the primary and secondary parameters, and the predictive distribution of the future value are then examined. Computations of the parameter estimates are found to be rather straightforward. Data from a performance test on pigs is analysed and discussed. We also discuss the difficulties involved in using a Lindley and Smith (1972) prior in this problem.     

Empirical Bayes estimates for correlated hierarchical data with overdispersion

An extension of the generalized linear mixed model was constructed to simultaneously accommodate overdispersion and hierarchies present in longitudinal or clustered data. This so‐called combined model includes conjugate random effects at observation level for overdispersion and normal random effects at subject level to handle correlation, respectively. A variety of data types can be handled in this way, using different members of the exponential family. Both maximum likelihood and Bayesian estimation for covariate effects and variance components were proposed. The focus of this paper is the development of an estimation procedure for the two sets of random effects. These are necessary when making predictions for future responses or their associated probabilities. Such (empirical) Bayes estimates will also be helpful in model diagnosis, both when checking the fit of the model as well as when investigating outlying observations. The proposed procedure is applied to three datasets of different outcome types. Copyright © 2014 John Wiley & Sons, Ltd.     

Empirical bayesInterval estimates: An application to geographical epidemiology

Summary Empirical Bayes estimates have been advocated as an improvement for mapping rare diseases or health events aggregated in small areas. In particular different parametric approaches have been proposed for dealing with non-normal data, assuming that disease occurrencies follow non-homogeneous Poisson law, whose parameters are treated as random variables. This paper shows how to conduct a complete Empirical Bayes analysis under an exchangeable model in the context of Geographical Epidemiology. Three different approaches for defining confidence limits obtained using a parametric bootstrap are compared: method 1 relies only on the first and second moment of the bootstrapped posterior distributions; method 2 computes the centiles of the bootstrapped posteriors; method 3 equates to α the average of the probabilities derived from the estimated bootstrapped cumulative posterior distributions. The simple Poisson-Gamma formulation was used to model mortality data on Larynx Cancer in the Local Health Units of Tuscany (1980–82 males). Two areas of significant elevated risk are identified.     

The empirical Bayes estimators of the mean and variance parameters of the normal distribution with a conjugate normal-inverse-gamma prior by the moment method and the MLE method

Most of the samples in the real world are from the normal distributions with unknown mean and variance, for which it is common to assume a conjugate normal-inverse-gamma prior. We calculate the empirical Bayes estimators of the mean and variance parameters of the normal distribution with a conjugate normal-inverse-gamma prior by the moment method and the Maximum Likelihood Estimation (MLE) method in two theorems. After that, we illustrate the two theorems for the monthly simple returns of the Shanghai Stock Exchange Composite Index.     

Turing’s anticipation of empirical bayes in connection with the cryptanalysis of the naval enigma *

The Enigma was a cryptographic (enciphering) machine used by the German military during WWII. The German navy changed part of the Enigma keys every other day. One of the important cryptanalytic attacks against the naval usage was called Banburismus, a sequentiai Bayesian procedure (anticipating sequential analysis) which was used from the sorine of 1941 until the middle of 1943. It was invented mainlv bv A. M. Turina and was perhaps the first important sequential Bayesian IE is unnecessab to describe it here. Before Banburismus could be started on a given day it was necessary to identifv which of nine ‘biaram’ (or ‘diaraph’) tables was in use on that day. In Turing’s approach to this identification hk had io istimate the probabilities of certain ‘trigraphs’. rrhese trigraphs were used. as described below. for determinine the initial wheel settings of messages). For estimatidg the probabilities, Turing inventedin important special case o the nonparametric (nonhypermetric) Empirid Bayes method independently of Herbert Robbins. The techniaue is the sumxisine form of Emdrical Baves in which a physical prior is assumed to eist but no apbroxiGate functional fonn is assumed for it.