2 research outputs found
Maximum a posteriori estimation for Markov chains based on Gaussian Markov random fields
In this paper, we present a Gaussian Markov random field (GMRF) model for the transition
matrices (TMs) of Markov chains (MCs) by assuming the existence of a neighborhood relationship
between states, and develop the maximum a posteriori (MAP) estimators under different
observation conditions. Unlike earlier work on TM estimation, our method can make full use of
the similarity between different states to improve the estimated accuracy, and the estimator can
be performed very efficiently by solving a convex programming problem. In addition, we discuss
the parameter choice of the proposed model, and introduce a Monte Carlo cross validation
(MCCV) method. The numerical simulations of a diffusion process are employed to show the
effectiveness of the proposed models and algorithms