Upper and Lower Probability Inferences for the Logistic Function

Abstract

A general system of inference which leads to upper and lower posterior distributions based on sample data has been proposed by Dempster (1967). This general theory of inference is applied to the two-parameter logistic function, given the data from independent binomial populations. Inferences are developed for fixed regions about the two parameters and about interesting combinations of these parameters. The resulting upper and lower probabilities are generated by a random polygonal-type region, or more exactly by specific extreme points of this region. For these extreme points, the exact marginal and joint distributions are derived; approximate distributions are also derived.