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

作     者：Chen, Nan Giannakis, Dimitrios Herbei, Radu Majda, Andrew J. 

作者机构：NYU Dept Math 550 1St Ave New York NY 10012 USA NYU Courant Inst Math Sci Ctr Atmosphere Ocean Sci New York NY 10012 USA Ohio State Univ Dept Stat Columbus OH 43210 USA 

出 版 物：《SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION》 (SIAM/ASA不确定性量化杂志)

年 卷 期：2014年第2卷第1期

页      面：647-669页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：ONR-MURI [N00014-12-1-0912] National Science Foundation [DMS-1209142] Direct For Mathematical & Physical Scien Division Of Mathematical Sciences Funding Source: National Science Foundation 

主　　题：hidden process intermittency stochastic parameterized model data augmentation MCMC algorithm prediction skill 

摘      要：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.