Description
Finite mixtures of distributions have provided a mathematical-based approach to the statistical modeling of a wide variety of random phenomena. Because of their usefulness as an extremely flexible method modeling, finite mixture modes have continued to receive increasing attention over the years, both from a practical and theoretical point of view. Indeed, in the past decade the extent and the potential of the applications of finite mixture models have widened considerably. Fields in which mixture models have been successfully applied include astronomy, biology, economics, engineering, genetics, marketing, medicine, and psychiatry, among many other fields in the biological, physical, and social sciences. In these applications, finite mixture models underpin a variety of techniques in image analysis, and survival analysis, in addition to their more direct role in data analysis and inference of providing descriptive models for distributions.
Even with the advent of high-speed computers, there had been some reluctance in the past to fit mixture models to data of more than one dimension, possibly because of a lack of understanding of issues that arise with their fitting. They include the presence of multiple maxima in the mixture likelihood function and the unboundedness of the likelihood function in he case of normal components with unequal covariance matrices. But as the difficulties concerning these computational issues became to be properly understood and successfully addressed, it has led to the increasing use of mixture models in practice.
In this workshop, we shall provide an account of the major issues involved with modeling via finite mixture distributions. The emphasis is to be on the applications of finite mixture models, but there will be coverage of some of the important theoretical problems still to be resolved. The wide applicability of finite distributions for modeling random phenomena will be illustrated by their application to a variety of data sets arising from the various sciences. There is now available a number of software packages on the Web for the fitting of mixture models. A survey of these packages will be given in the workshop with particular emphasis on the presenter's own package called EMMIX. The latter has been substantially updated since JSM2000.
The workshop is aimed at statisticians in general, as well as to investigators working in the many diverse areas in which relevant use can be made of finite mixture models. Although it is anticipated that many in the audience will have majored in statistics, only a working knowledge of statistics will be needed to participate in the workshop.
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