Fast Bayesian reconstruction of chaotic dynamical systems via extended Kalman filtering

We present an improved Markov chain Monte Carlo (MCMC) algorithm for posterior computation in chaotic dynamical systems. Recent Bayesian approaches to estimate the parameters of chaotic maps have used the Gibbs sampler which exhibits slow convergence due to high posterior correlations. Using the extended Kalman filter to compute the likelihood function by integrating out all unknown system states, we obtain a very efficient MCMC technique. We compare the new algorithm to the Gibbs sampler using the logistic, the tent, and the Moran-Ricker maps as applications, measuring the performance in terms of CPU and integrated autocorrelation time.