Panagiotis Andreou
UNC-Chapel Hill

Bayesian Bootstrap for the Transition Matrix of Finite State-Space Markov Chains

We study the problem of estimating the transition probability matrix on the context of a discrete-time finite state-space Markov chain, based on an observed path of the chain. We briefly describe the asymptotic, as well as the frequentist bootstrap approach to the problem. Bayesian bootstrap is then introduced, first for independent and then for data from a Markov Chain. The Bayesian bootstrap estimator satisfies desired properties, such as the Lindeberg Central Limit Theorem. Finally, we provide a short simulation analysis to compare the Bayesian bootstrap with the asymptotic estimator

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