Grant: Discovery Grants Program - Individual

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.