RECENT DEVELOPMENTS IN COMPUTER-ASSISTED ANALYSIS OF MIXTURES

This paper reviews recent developments in the area of computer-assiste d analysis of mixture distributions (C.A.MAN). Given a biometric situa tion of interest in which, under homogeneity assumptions, a certain pa rametric density occurs, such as the Poisson, the binomial, the geomet ric, the normal, and so forth, then it is argued that this situation c an easily be enlarged to allow a variation of the scalar parameter in the population. This situation is called unobserved heterogeneity. Thi s naturally leads to a specific form of nonparametric mixture distribu tion that can then be assumed to be the standard model in the biometri c application of interest (since it also incorporates the homogeneous situations as a special case). Besides developments in theory and algo rithms, the work focuses on developments in biometric applications suc h as meta-analysis, fertility studies, estimation of prevalence under clustering, and estimation of the distribution function of survival ti me under interval censoring. The approach is nonparametric for the mix ing distribution, including leaving the number of components (subpopul ations) of the mixing distribution unknown.