An MCMC Algorithm for Parameter Estimation in Signals with Hidden Intermittent Instability

Prediction of extreme events is a highly important and challenging problem in science, engineering, finance, and many other areas. The observed extreme events in these areas are often associated with complex nonlinear dynamics with intermittent instability. However, due to lack of resolution or incomplete knowledge of the dynamics of nature, these instabilities are typically hidden. To describe nature with hidden instability, a stochastic parameterized model is used as the low-order reduced model. Bayesian inference incorporating data augmentation, regarding the missing path of the hidden processes as the augmented variables, is adopted in a Markov chain Monte Carlo (MCMC) algorithm to estimate the parameters in this reduced model from the partially observed signal. Howerver, direct application of this algorithm leads to an extremely low acceptance rate of the missing path. To overcome this shortcoming, an efficient MCMC algorithm which includes a pre-estimation of hidden processes is developed. This algorithm greatly increases the acceptance rate and provides the low-order reduced model with a high skill in capturing the extreme events due to intermittency.