Modeling of Imperfect Data in Medical Sciences by Markov Chain with Numerical Computation

In this paper we consider sequences of observations that irregularly space at infrequent time in-tervals. We will discuss about one of the most important issues of stochastic processes, named Markov chains. We would reconstruct the collected imperfect data as a Markov chain and obtain an algorithm for finding maximum likelihood estimate of transition matrix. This approach is known as EM algorithm, which includes main optimum advantages among other approaches, and consists of two phases: phase (maximization of target function). Continue the phase E and M to achieve the sequence convergence of matrix. Its limit is the optimal estimator. This algorithm, in contrast with other optimum algorithms which could be used for this purpose, is practicable in maximum likelihood estimate, and unlike to the methods which involve mathematical, is executable by computer. At the end we will survey the theoretical outcomes with numerical computation by using R software.