Bayesian estimation for stochastic dynamic equations via Fokker–Planck equation

Abstract

A Bayesian approach is proposed to estimate unknown parameters in stochastic dynamic equations (SDEs). The Fokker–Planck equation from statistical physics method is adopted to calculate the quasi-stationary probability density function. A hybrid algorithm combining the Gibbs sampler and the Metropolis–Hastings (MH) algorithm is proposed to obtain Bayesian estimates of unknown parameters in SDEs. Three simulation studies of SDEs are conducted to investigate the performance of the proposed methodologies. Empirical results evidence that the proposed method performs well in the sense that Bayesian estimates of unknown parameters are quite close to their corresponding true values and their corresponding standard divinations are quite small, and the computational accuracy of normalization parameters strongly affects the accuracy of the proposed Bayesian estimates.