Speaker: Yariv Ephraim, GMU

Title: Parameter estimation of Markov modulated processes

Abstract: A Markov modulated process is a doubly stochastic random process with an underlying continuous-time finite-state homogeneous Markov chain. The processes in this class differ in their observable process. In this talk we focus on the Markov modulated Markov process. Here, the observable process is a conditionally continuous-time finite-state non-homogeneous Markov chain given the underlying chain. The generator of the observable process at any given time is determined by the state of the underlying Markov chain at that time. The parameter of the process comprises the set of generators for the two Markov chains. We derive joint likelihood functions for the underlying and observable processes, and use them in an EM approach for estimating the parameter of the process. The approach we describe generalizes an earlier approach developed by Ryd\'{e}n for Markov modulated Poisson processes. For the latter case, the observable process is conditional Poisson. The approach is also appl icable to Markov modulated Gaussian processes. Markov modulated processes have many applications in queuing theory, communication networks, phylogenetics, and ion channel currents estimation. This is a joint work with William Roberts.

Bio: Yariv Ephraim received the D.Sc. in Electrical Engineering in 1984 from the Technion-Israel Institute of Technology, Haifa, Israel. He has been with George Mason University, Fairfax, Virginia, since 1991, where he is Professor of Electrical and Computer Engineering. During 1985-1993 he was a Member of Technical Staff at AT\&T Bell Labs, Murray Hill, New Jersey. During 1984-1985 he was a Rothschild Post-Doctoral Fellow at Stanford University, Palo Alto, Calif

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491