ABB  Vol.5 No.13 , November 2014
Modeling of Imperfect Data in Medical Sciences by Markov Chain with Numerical Computation
Abstract: 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.
Cite this paper: Afshari, M. and Ghaffaripour, A. (2014) Modeling of Imperfect Data in Medical Sciences by Markov Chain with Numerical Computation. Advances in Bioscience and Biotechnology, 5, 1003-1008. doi: 10.4236/abb.2014.513114.

[1]   Dempstr, A.P., Larid, N.M. and Rubin, D.B. (1997) Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society, 39, 1-38.

[2]   Raj, B. (2002) Asymmetry of Business Cycles: The Markov-Switching Approach, Soft-Tissue Material Properties Under Large Deformation: Strain Rate Effect. Hand Book of Applied Econometrics and Statistical Inference, 3, 687-710.

[3]   Johnson, C. and Gallivan, S. (1995) Estimating a Markov Transition Matrix from Observational Data. Journal of the Operational Researches Society, 46, 405-410.

[4]   Melichson, I. (1999) A Fast Improvement to the EM Algorithm on the Own Terms. Journal of the Royal Statistical Society—Series B, 51, 127-138.

[5]   Cappee, O., Moulines, E. and Ryden, T. (2005) Inference in Hidden Markov Models. Springer, New York.

[6]   Chib, S. (1996) Calculating Posterior Distributions and Modal Estimates in Markov Mixture Models. Journal of Econometrics, 75, 79-97.

[7]   Roberts, W. and Ephraim, Y. (2008) An EM algorithm for Ion Chanel Current Estimation. IEEE Transactions on Signal Processing, 56, 26-35.