POWRE: Problems in Classification and Clustering

混合分布已被广泛用作模型，在这种情况下，数据被视为来自由不同比例混合的几个亚种群组成的种群。混合模型的应用涵盖了广泛的领域：遥感、农业、电泳、医学诊断和预后、地球研究、抽样、人口多样性、市场研究、图像增强和图像编码、人类和动物感知、经济学、遗传学、电泳等等。研究将集中在三个主要领域。首先，将Cordero Brana关于最小海灵格距离估计的工作从单变量混合模型推广到多变量情况。这将涉及研究和推导一个适当的多元密度估计混合模型，以及考虑它的计算方面。研究了HMIX算法和自适应密度估计器的收敛性。这种方法的优点是，与最大似然方法不同，它产生的估计对数据污染的存在既有效又稳健。其次，申请人将考虑使用BRM-IS算法计算后验分布。该方法类似于Newton和Raftery（1994）的加权似然Bootstrap （WLB）过程，但BRM-IS在数据不完整的情况下更好，因为它考虑了感兴趣参数的先验分布。BRM已成功地应用于删减威布尔模型、具有威布尔分布的失效模型以及混合分布的（单变量）混合。该计划是与Gilles Celeux博士和他在法国国家计算机科学与控制研究所（INRIA Rhone-Alpes, France）的研究小组一起开展这项工作。该power项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）联合支持

Mixtures distributions have been used extensively as models in situations where data are viewedas 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 afew.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 theadaptive density estimator will be studied. The advantage of this method is that it produces estimates thatare 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).>