Some unimodality properties of likelihoods derived from grouped data

This paper considers unimodality properties of certain likelihoods derived from grouped data. Three main types of model are considered: exponential families, linear models and empirical Bayes models. Partial answers are offered to questions raised in recent papers and areas needing further clarification are indicated. The paper shows that a link between the models is a theorem given by Prekopa on strongly unimodal probability densities and indicates ways of using the theorem to formulate models for analysing grouped multimodal univariate data.