Recent developments in computer-assisted analysis of mixtures

This paper reviews recent developments in the area of computer-assisted analysis of mixture distributions (C.A.MAN). Given a biometric situation of interest in which, under homogeneity assumptions, a certain parametric density occurs, such as the Poisson, the binomial, the geometric, the normal, and so forth, then it is argued that this situation can easily be enlarged to allow a variation of the scalar parameter in the population. This situation is called unobserved heterogeneity. This naturally leads to a specific form of nonparametric mixture distribution that can then be assumed to be the standard model in the biometric application of interest (since it also incorporates the homogeneous situations as a special case). Besides developments in theory and algorithms, the work focuses on developments in biometric applications such as meta-analysis, fertility studies, estimation of prevalence under clustering, and estimation of the distribution function of survival time under interval censoring. The approach is nonparametric for the mixing distribution, including leaving the number of components (subpopulations) of the mixing distribution unknown.