Estimating parameters of Lorenz chaotic system with MCMC method

Based on Bayesian theorem, a method is proposed to estimate the unknown parameters of Lorenz chaotic system using Markov Chain Monte Carlo (MCMC) method. Firstly, the posterior probability density function for unknown parameters is deduced. Secondly, taking the posterior probability as the invariant distribution, the Adaptive Metropolis algorithm is used to construct the Markov Chains. Thirdly, the converged samples are used to calculate the mathematic expectation of the unknown parameters. The results of numerical experiments show that the parameters estimated by the new method have high precision and the noise is filtered effectively from observations at the same time.