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

Gaussian Markov transition models of molecular kinetics

The slow processes of molecular dynamics (MD) simulations—governed by dominant eigenvalues and eigenfunctions of MD propagators—contain essential information on structures of and transition rates between long-lived conformations. Existing approaches to this problem, including Markov state models and the variational approach, represent the dominant eigenfunctions as linear combinations of a set of basis functions. However the choice of the basis functions and their systematic statistical estimation are unsolved problems. Here, we propose a new class of kinetic models called Markov transition models (MTMs) that approximate the transition density of the MD propagator by a mixture of probability densities. Specifically, we use Gaussian MTMs where a Gaussian mixture model is used to approximate the symmetrized transition density. This approach allows for a direct computation of spectral components. In contrast with the other Galerkin-type approximations, our approach can automatically adjust the involved Gaussian basis functions and handle the statistical uncertainties in a Bayesian framework. We demonstrate by some simulation examples the effectiveness and accuracy of the proposed approach