Estimating the Transitional Probabilities of the E.Coli Gene Chain by Maximum Likelihood Method and Bayes Method

The transition matrix estimators of the Markov chain are not accurate and the transition matrix is considered given. There are many methods that are used to estimate the transition probabilities matrix for different cases, the most famous of which is the Maximum Likelihood Method, In order to find a good estimator for the transition probabilities matrix of the Markov chain, a Bayes method and a Proposed Method was used in this paper, to reach the transition probabilities with the least variance, The Escherichia Coli (E.Coli) gene chain was chosen as an applied aspect of the study due to its importance in medical research and for the purpose of discovering and manufacturing treatments by knowing the final form of its gene chain. After testing the E.Coli gene chain, it was found that is represents a Markov chain, and then both the transition probabilities matrix and the transition probabilities variance were estimated used Proposed Method and Bayes method and Maximum Likelihood Method, and it was found that the Proposed Method for transitional probabilities is better than the Bayes method and Maximum Likelihood Method dependence on the variance.