Bayesian Model Selection for Partially Observed Markov Process with Three States

Student: Glukhova Elena

Educational Programme: Mathematical Methods of Optimization and Stochastics (Master)

Final Grade: 8

Year of Graduation: 2017

In this paper we consider the problem of choosing the parameters of a hidden Markov model using the Bayesian approach. A hidden discrete Markov chain (DMC) with three states and symmetric and rare transitions is considered. The observed values are obtained as hidden values of the DMC, noisy with normal homogeneous noise (with a known dispersion). Since the obtaining of the likelihood function (and as a consequence of the a posteriori distribution) is analytically difficult, the paper attempts to use the Monte Carlo methods for this task according to the scheme of Markov chains, namely the Gibbs-sampling. The influence of the parameters of the prior distribution on the accuracy of the obtained estimate is also checked.

Full text (added May 29, 2017)

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