Finite mixture models are widely used in scientific investigations. In one of the earliest examples, Karl Pearson fitted a two-component normal mixture model to 1000 measurements of crabs, indicating the existence of two species in the population. In general, mixture models are used to model scenarios in which certain variables are measured but a categorical variable is missing. For example, the patient population may be divided into several subpopulations according to their genetic make-up, but the make-up is yet to be determined. Mixture-type scenarios include hidden Markov models, in which the missing variable follows a Markov chain model; and latent structure models, in which the missing variable or variables represent model-enriching devices. Mixture models can simply be employed as a more flexible parametric or nonparametric description of data, processes, and systems.
The parameters of interest of finite mixture models are often at the boundary of the parameter space. They generally loss identifiability when the parameter space is expanded. Such non-regularity invariably leads to technical challenges in designing valid and effective data analysis procedures. However, after many decades of effort, we have witnessed substantial progresses in many fronts. We now have easy-to-use packages to fit both nonparametric and finite mixture models. The consistency of the maximum likelihood estimator in many situations has been established. We have detailed characterizations of the model identifiability. We have clear descriptions of the large sample properties of the likelihood ratio tests for the order of mixture models. The Bayesian approach to finite mixture models has overcome many obstacles and gained popularity in applications. The inventions of the modified likelihood ratio test and the EM-test, in particular, make it possible to rigorously assess the order of the finite mixture models.
Researchers in the area of mixture models spread all over the world. This conference aims to provide a rare platform for top researchers in this area to exchange ideas under the same roof. This is also a great opportunity for Chinese researchers to mingle with world-famous experts. Through small-scale conferences of this nature, we hope to extend the horizon of the research area of the Chinese statisticians and to promote the research activities in the area of finite mixture models.
The conference will be held at Guangxi Normal University, Guilin, Guangxi, China, from Aug 12-16, 2018 and the conference website is http://www.math.gxnu.edu.cn/conf2018/