Finite mixture models and their applications

有限混合模型广泛应用于多个均匀总体混合在一起的数据集。在金融经济学中，由于存在三种风险机制：低、正态和高，因此经常将三种正态分布的混合物应用于股票的日收益。有限混合中均匀总体的数量在应用中具有很大的意义。例如，在统计遗传学中，这个数字反映了起作用的主要基因的数量。在第一个项目中，将开发一种新颖且实际方便的方法，称为em测试，用于测试有限混合物中均匀种群的数量。

Finite mixture models are widely applied to data sets in which several homogeneous populations are mixed together. In financial economics, mixtures of three normal distributions are often applied to daily stock returns due to the existence of three risk regimes: low, normal and high. The number of homogeneous populations in a finite mixture is of great interest in applications. For example in statistical genetics, this number reflects the number of major genes in action. In the first project, a novel and practically convenient method, called the EM-test, will be developed for testing the number of homogeneous populations in a finite mixture.