A Bayesian Nonparametric Model for Spectral Estimation of Metastable Systems

Abstract

The identification of eigenvalues and eigenfunc-tions from simulation or experimental data is a fundamental and important problem for anal-ysis of metastable systems, because the domi-nant spectral components usually contain a lot of essential information of the metastable dy-namics on slow timescales. It has been shown that the dynamics of a strongly metastable sys-tem can be equivalently described as a hidden Markov model (HMM) under some technical as-sumptions and the spectral estimation can be performed through HMM learning. However, the spectral estimation with unknown number of dominant spectra is still a challenge in the framework of traditional HMMs, and the infi-nite HMMs developed based on stick-breaking processes cannot satisfactorily solved this prob-lem either. In this paper, we analyze the diffi-culties of spectral estimation for infinite HMMs, and present a new nonparametric model called stick-breaking half-weighted model (SB-HWM) to address this problem. The SB-HWM defines a sparse prior of eigenvalues and can be applied to Bayesian inference of dominant eigenpairs of metastable systems in a nonparametric manner. We demonstrate by simulations the advantages of applying SB-HWM to spectral estimation. 1