POWRE: Problems in Classification and Clustering

混合分布被广泛地用作模型，在数据被看作是由不同比例混合的几个子总体组成的总体的情况下。混合模型的应用范围广泛：遥感、农业、电泳学、医学诊断和预测、地球研究、采样、种群多样性、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、电泳学等。研究将集中在三个主要领域。首先，将Cordero Brana关于最小Hellinger距离估计的工作从单变量混合模型推广到多变量混合模型。这将涉及研究和推导适用于混合模型的多变量密度估计器，并考虑其计算方面。此外，还将研究HMIX算法和自适应密度估计器的收敛性质。与最大似然法不同，这种方法的优点是它产生的估计对数据污染的存在既有效又稳健。其次，申请者将考虑使用BRM-IS算法来计算后验分布。该方法类似于牛顿和雷夫里(1994)的加权似然Bootstrap(WLB)方法，但BRM-IS方法在不完全数据的情况下更好，因为它考虑了感兴趣参数的先验分布。BRM已成功地应用于截尾威布尔模型、威布尔分布失效模型和混合分布的(单变量)混合分布。计划与Gilles Celeux博士和他在法国国家计算机科学与控制研究所(INRIA Rhone-Alpe)的研究团队一起开展这项工作。这个POWRE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).>