Improved Empirical Bayes Estimation in Group Testing Procedure for Small Proportions

Group testing has been long recognized as an efficient method to classify all the experimental units into two mutually exclusive categories: defective or not defective. In recent years, more attention has been brought to the estimation of the population prevalence rate p of a disease, or of some property, using group testing. In this article, we propose two scaled squared-error loss functions, which improve the Bayesian approach to estimating p in terms of minimizing the mean squared error (MSE) of the Bayes estimators of p for small p. We show that the new estimators are preferred over the estimator from the usual squared-error loss function and the maximum likelihood estimator (MLE) for small p.     

Bayes estimation of the binomial parameter n

Bayes estimation of the binomial parameter n based on a general prior distribution for n is studied. As special cases improper prior and Poisson prior (which is a natural choice) are considered, and formulae for the marginal and posterior distributions are obtained. It is shown that the assumption of improper priors in both p and n leads to implausible results.     

Preludes to Attainment: Race,Sex, and Student Achievement Orientations*

This paper investigates race-sex differences in achievement orientation using a national sample of high school seniors. Achievement orientation is approximated by attitudinal measures (educational expectations, occupational aspirations, academic self concept, self esteem, and locus-of-control) known to be correlated with expected and actual attainments. Three major sets of student background factors are related to ent orientation: (1) family SES, (2) school context, and (3) parental expectations. Race-sex comparisons of achievement orientation revealed several interesting, but few definitive differences. Occupational aspirations were a dimension of consistent differentiation: whites and males aspired to higher status, less stereotypic occupations than did blacks and females. Pronounced interpersonal effects are implied throughout, with family educational attainments, peer plans, teacher evaluations (grades) and parent aspirations strongly influencing achievement orientations in all race-sex subgroups. The paper calls for intensive, longitudinal studies of student interactions with parents, friends, teachers, and other individuals who influence their perceptions of what constitute desirable and possible future roles.     

Quasi-orderings and population ethics

Population ethics contains several principles that avoid the repugnant conclusion. These rules rank all possible alternatives, leaving no room for moral ambiguity. Building on a suggestion of Parfit, this paper characterizes principles that provide incomplete but ethically attractive rankings of alternatives with different population sizes. All of them rank same-number alternatives with generalized utilitarianism.This paper was presented to the conference Incommensurability and Value, Château du Baffy, Caen, April 1994, and an earlier version was presented at the Applied Ethics Centre of the University of British Columbia. We are indebted to John Broome, whose comments inspired this paper, Alan Gibbard, James Griffin, Peter Hammond, Adam Morton, Klaus Nehring, and conference and seminar participants for comments and suggestions. Financial support through a grant from the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged     

Ballot theorem and lattice path crossings

We consider lattice paths which cross the diagonal exactly r times, and by a simple method determine the number of such paths when the endpoint is given. Then as a byproduct we easily obtain Feller's (1968, p.84) result for crossings when the length is given.     

USING REPEATED MEASURES DESIGNS IN PROGRAM EVALUATION OF FAMILY THERAPY*

Data from 14 simulated families were analyzed with both a repeated measures and an ordinary analysis of variance design in order to illustrate the differences between the two approaches. The advantages of repeated measures designs for the analysis of family data in the program evaluation of family therapy are highlighted.