# Seminar in applied mathematics and statistics

SPEAKER: Budhi Surya (School of Mathematics and Statistics, Victoria University of Wellington, New Zealand).

TITLE: Exit time distributions of the finite mixture of Markov jump processes: properties and the EM estimation.

ABSTRACT:  In this talk, I will discuss properties and the EM estimation of the distribution of exit time to an absorbing state of the finite mixture of right-continuous Markov jump processes moving on a given finite state space. When the process is observed in a state or making a transition from one state to another, there is uncertainty associated with which underlying Markov process drives the movement of the process. Unlike its underlying, the mixture process does not have the Markov property. When conditioning on its past observations, Bayesian update of the exit time distribution is given explicitly in terms of the states the process has visited, the number of transitions between the states, the length of time the process stays in each state, and the intensity matrices of the underlying Markov processes. The prior (unconditional) distribution forms a generalized mixture of phase-type distributions. Explicit and closed form maximum likelihood estimates of the distribution parameters are presented. Under incomplete observations where either sample paths of the process or the exit times are available, the estimation is performed using the EM algorithm. Some Monte Carlo simulations are discussed to exemplify and validate the proposed algorithm.

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Upcoming events (after February 19):

Tuesday, March 3 at 13.15: Susanna Levantesi

Tuesday, March 3 at 14.15: Massimiliano Menzietti

Tuesday, March 3 at 15.15: Valeria D'AMATO

Wednesday, March 18 at 15.15: Alexandre Antonov

Friday, April 17 at 13.15: Thomas S Richardson
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