Review Of The Finite Mixture Models And Their Applications

This paper emphasizes on the study of finite mixture models and its application in biology. In this paper the more recent work is surveyed against the background of the existing literature. The widespread use od mixture models in recent times is demonstrated by the amount of references in this paper. A comprehensive account of the major issues involved with modelling via finite mixture distributions is provided. They include identifiability problems;the actual fitting of finite mixtures through use of the EM algorithm and we also consider the Bayesian estimation of mixture models and others random algorithms;the properties of the maximum likkelihood estimators so obtained, the assessment of the number of components to be used in the mixture, and the applicability of asymptotic theory in providing a basis for the solutions to some of these problems. In order to provide some basic guidelines to users of mixture models on some biological issuse, we provide some examples and methods on the applications of the mixtures.This paper also covers the latest developments on existing issues with mixture modeling,such as assessing the number of components to be used in a mixture model and associated problem of determining how many clusters there are in clustering applications with mixture models. Expecially the problem of testing the hypothesis about the number of the components is studied. There has been no general statistical testing procedure for this problem . A modified likelihood ratio statistic where under the null and the alternative hypotheses estimates of the parameters are obtained from a modified likelihood function. It is shown that The asymptotic null distribution of the modified likelihood ratio test proposed is derived and found to be relatively simple and easily applied.