Developments and challenges in mixture models

混合模型的发展和挑战

• 批准号: RGPIN-2018-05846
• 负责人: Fu, Yuejiao
• 金额: $ 1.17万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=713012
• 关键词: Developments; challenges; mixture; models

Mixture models provide extremely flexible and effective means of handling heterogeneity in data. However, statistical inference for mixture models is particularly challenging due to the irregularity of the problem from a classical parametric likelihood inference point of view. Therefore, mixture models are often viewed as one of the most important classes of non-regular statistical models. Despite the extremely wide applications of mixture models, research in statistical theory and methods on mixture models is still limited. The proposed research program aims to develop innovative methodologies in the field of mixture models and to use such methodologies in solving statistical problems in the presence of heterogeneity. The short-term objectives are to investigate inference on the order of general location-scale mixtures; to develop theory and methodologies for finite mixtures of gamma distributions; and to explore the use of mixture models in DNA methylation studies. The proposed research program will significantly enhance the current research on mixture models, especially the fundamental inference problems on various aspects of finite mixture models. The proposed research is motivated by my ongoing and future collaborations arising from problems in genetics, biology, engineering, medicine, and finance. The potential research outcomes will provide new insights and useful guidance for the analysis of heterogeneous data.

混合模型提供了处理数据异质性的极其灵活且有效的方法。然而，混合模型的统计推断是特别具有挑战性的，由于从经典的参数似然推断的角度来看，问题的不规则性。因此，混合模型通常被视为最重要的一类非正则统计模型。尽管混合模型有着极其广泛的应用，但关于混合模型的统计理论和方法的研究还很有限。拟议的研究计划旨在开发混合模型领域的创新方法，并使用这种方法来解决异质性存在的统计问题。短期目标是调查一般位置尺度混合物的顺序上的推断;开发有限混合伽马分布的理论和方法;并探索在DNA甲基化研究中使用混合模型。该研究计划将大大提高目前的研究混合模型，特别是有限混合模型的各个方面的基本推理问题。这项研究的动机是我正在进行的和未来的合作，这些合作涉及遗传学、生物学、工程学、医学和金融等领域的问题。这些潜在的研究成果将为异构数据的分析提供新的见解和有用的指导。