Parallel probabilistic graphical model approach for nonparametric Bayesian inference

We propose an efficient uncertainty quantification framework that makes use of multiple probabilistic graphical models to yield a nonparametric Gaussian mixture description of the target probability distribution. The methodology is indeed generic, but this work focuses on its application to the particular class of the inference problems arising from the hidden Markov process and the associated observations in a sequence. The implementation procedure is demonstrated with the dynamical system models in both low and high dimension. In case of the low dimension, it is shown that the usual factor graph for the sequential data can be used to produce a very accurate approximate solution. However, for high dimensional systems, a new family of the factor graphs are developed in order to achieve an effective dimension reduction and to facilitate a synergetic application together with multiple graphs in addressing the Bayesian data assimilation. As a result, a new paradigm for the probabilistic filtering and smoothing emerges, and the applicability of the graphical model approach has been broadened.