Bayesian Estimation in Stochastic Differential Equation Models via Laplace Approximation

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• 作者：Hadiseh Karimi ^{hadiseh.karimi@queensu.ca" class="auth_mail" title="E-mail the corresponding author} ; Kimberley B. McAuley ^{kim.mcauley@queensu.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Parameter estimation ; stochastic modeling ; stochastic systems ; likelihood ; nonlinear equations ; uncertain dynamic systems ; differential equations
• 刊名：IFAC-PapersOnLine
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：49
• 期：7
• 页码：1109-1114
• 全文大小：599 K

文摘

A Bayesian algorithm is developed for estimating measurement noise variances, disturbance intensities and model parameters in nonlinear stochastic differential equation (SDE) models of interest to chemical engineers. The proposed Bayesian algorithm uses prior knowledge about parameters and builds on the Laplace Approximation Maximum Likelihood Estimation (LAMLE) algorithm (Karimi and McAuley, 2014). The effectiveness of the proposed algorithm is compared with LAMLE using a nonlinear continuous stirred tank reactor (CSTR) model. Parameter estimation using 2000 simulated datasets reveals that the proposed method provides more precise and less biased estimates, especially for small data sets.