Mixtures distributions have been used extensively as models in situations where data are viewed as arising from a population that is comprised of several subpopulations mixed in varying proportions. Applications of mixture models covers a wide variety of fields: remote sensing, agriculture, electrophoresis, medical diagnosis and prognosis, earth studies, sampling, population diversity, marketing research, image enhancing and picture coding, human and animal perception, economics, genetics, electrophoresis to name a few.
The research will focus on three major areas. First,it will extend the work of Cordero Brana on minimum Hellinger distance estimation from univariate mixture models to the multivariate case. This will involve investigating and deriving an appropriate multivariate density estimator for mixture models as well as considering the computational aspects of it. Also convergence properties of the HMIX algorithm and the adaptive density estimator will be studied. The advantage of this method is that it produces estimates that are both efficient and robust to the presence of data contamination unlike maximum likelihood methods.
Second, the applicant will consider BRM-IS algorithm for computing posterior distributions. The method is similar to the Weighted Likelihood Bootstrap (WLB) procedure of Newton and Raftery (1994) but BRM-IS is better in the case of incomplete data since it takes into account the prior distribution of the parameters of interest. BRM has been successfully applied to censored Weibull models, failure models with Weibull distributions and to (univariate) mixtures of mixture distributions.
The plan is to carry out this work with Dr. Gilles Celeux and his research team at the National Institute for Research in Computer Science and Control (INRIA Rhone-Alpes, France).
This POWRE project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).
