Showing papers by "Donald B. Rubin published in 1981"

The Bayesian Bootstrap

Abstract: The Bayesian bootstrap is the Bayesian analogue of the bootstrap. Instead of simulating the sampling distribution of a statistic estimating a parameter, the Bayesian bootstrap simulates the posterior distribution of the parameter; operationally and inferentially the methods are quite similar. Because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions, neither method should be applied without some consideration of the reasonableness of these model assumptions. In this sense, neither method is a true bootstrap procedure yielding inferences unaided by external assumptions.

Estimation in Covariance Components Models

Abstract: Estimation techniques for linear covariance components models are developed and illustrated with special emphasis on explaining computational processes. The estimation of fixed and random effects when the variances and covariances are known is presented in Bayesian terms, Point estimates of the unknown variances and covariances are computed using the EM algorithm for maximum likelihood estimation from incomplete data. The techniques are illustrated with data on law schools, field mice, and professional football teams.

Estimation in Parallel Randomized Experiments

Abstract: Many studies comparing new treatments to standard treatments consist of parallel randomized experiments. In the example considered here, randomized experiments were conducted in eight schools to determine the effectiveness of special coaching programs for the SAT. The purpose here is to illustrate Bayesian and empirical Bayesian techniques that can be used to help summarize the evidence in such data about differences among treatments, thereby obtaining improved estimates of the treatment effect in each experiment, including the one having the largest observed effect. Three main tools are illustrated: 1) graphical techniques for displaying sensitivity within an empirical Bayes framework, 2) simple simulation techniques for generating Bayesian posterior distributions of individual effects and the largest effect, and 3) methods for monitoring the adequacy of the Bayesian model specification by simulating the posterior predictive distribution in hypothetical replications of the same treatments in the same eig...

The graduate management admission test prediction bias study

Abstract: This document presents the results of an investigation into the prediction of first-year average in graduate management school based on undergraduate grade point average and GMAT scores. It is found that the use of a single prediction equation for both black students and white students tends to produce over predictions of the former's graduate school performance. Substantial effort is devoted to developing a prediction system which takes into account ethnic status. This approach is made practicable by employing the empirical Bayes estimation paradigm, and the new predictions represent a substantial improvement over the ones based on a single equation for both races.

Fitting Additive Models to Unbalanced Two-Way Data.

Abstract: A time-saving and space-saving algorithm is presented for computing the sums of squares and estimated cell means under the additive model in a two-way analysis of variance or co-variance with unequal numbers of observations in the cells. The algorithm uses matrices of order no larger than min{r,c}, where r = number of rows and c = number of columns. A Fortran program is available; the key computational device is a special subroutine, LS2WAY, whose FORTRAN code appears in Rubin, Stroud & Thayer (1978). The procedure is illustrated using high school and college numerical grade averages for 85 feeder high schools over a period of 6 years.