Some Statistical Methods in Genetics

A challenging problem in modern genetics is to identify the collection of factors responsible for increasing the risk of specified complex diseases. The progress in the human genome reading permitted to collect the genetic datasets for analysis by means of various complementary statistical tools. The intensive studies in this research domain are carried out in leading research centers all over the world. One has to operate with data of huge dimensions and this is one of the main difficulties in detection of genetic susceptibility to common diseases such as hypertension, myocardial infarction and others. In this chapter, we concentrate on the multifactor dimensionality reduction method, and we also discuss its modifications and extensions. Our recent results on the central limit theorem related to this method are provided as well. Moreover, we explain the main features of the logic regression where we tackle the simulated annealing for stochastic minimization of functions defined on a graph with forests as vertices. Finally, we mention several important research directions which are out of the scope of the present chapter.