Budhi Surya (VUW)

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Budhi Surya

Statistics

A seminar by Budhi Surya from Victoria University of Wellington

Title: First-exit time distribution 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 first-exit time distribution of a continuous-time stochastic process with a finite state space. The process is constructed by a finite mixture of right-continuous Markov jump processes moving at different speeds, represented by intensity matrices, on a given finite state space with one absorbing state. 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, i.e., the speed regime is unobservable. Unlike its underlying, the process itself is non-Markov. Distributional properties of the first-exit time to absorbing state is discussed. When conditioning on past observations of the process, Bayesian update of the first-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 stay in each state, and the intensity matrices of the underlying Markov processes. The prior distribution forms a (generalized) mixture of phase-type distributions. Maximum likelihood estimation of the distribution parameters based on complete and incomplete observations is presented in the closed-form. Under incomplete observations where only sample paths of the process or the exit times are available, the estimation is performed using the EM algorithm. Some Monte Carlo simulations are performed to check the validity of the proposed algorithm.     

Start date:

11am Thursday, 1 Aug 2019

End date:

12pm Thursday, 1 Aug 2019

Venue:

CBE LT1

Presenter(s):

Budhi Surya

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