605 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
A flat Dirichlet process switching model for Bayesian estimation of hybrid systems
AbstractHybrid systems are often used to describe many complex dynamic phenomena by combining multiple modes of dynamics into whole systems. In this paper, we present a flat Dirichlet process switching (FDPS) model that defines a prior on mode switching dynamics of hybrid systems. Compared with the classical Markovian jump system (MJS) models, the FDPS model is nonparametric and can be applied to the hybrid systems with an unbounded number of potential modes. On the other hand, the probability structure of the new model is simpler and more flexible than the recently proposed hierarchical Dirichlet process (HDP) based MJS. Furthermore, we develop a Markov chain Monte Carlo (MCMC) method for estimating the states of hybrid systems with FDPS prior. And the numerical simulations of a hybrid system in different conditions are employed to show the effectiveness of the proposed approach
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