Recursive Estimation of Multivariate Markov Processes – Yariv Ephraim (George Mason University)
A multivariate Markov process is a vector of random processes which are jointly, but not necessarily individually, Markov. Multivariate Markov processes form a rich family of mathematically tractable models, which have been found useful in numerous applications. Examples include the hidden Markov process in discrete-time, and the Markov modulated Poisson process in continuous-time. Multivariate Markov processes lend themselves to the mathematical tractability of Markov processes while allowing non- Markovian features for the individual process components. For example, while the distribution of the sojourn time of a multivariate Markov chain in each of its states is geometric or exponential, the distribution of the sojourn time of an individual process component in each of its states is phase-type. In this talk we present forward recursions for estimating some statistics of bivariate Markov chains, and of bivariate Markov chains observed through memoryless channels. We demonstrate the use of these forward recursions in an online algorithm for estimating the parameter of the process. Recursions for discrete-time as well as continuous-time multivariate Markov processes will be discussed.
This presentation is based on joint work with Brian L. Mark. This work was supported in part by the National Science Foundation under grant CCF- 0916568.
Yariv Ephraim received the D.Sc. degree in electrical engineering from the Technion-Israel Institute of Technology, Haifa, Israel, in 1984. From 1984-1985 he was a Rothschild Postdoctoral Fellow at the Information Systems Laboratory, Stanford University, Stanford, CA. From 1985 to 1993 he was a Member of Technical Staff at the Information Principles Research Laboratory, AT&T Bell Laboratories, Murray Hill, NJ. In 1991 he joined George Mason University, Fairfax, VA, where he currently is Professor of Electrical and Computer Engineering.