论文标题
使用汉密尔顿蒙特卡洛的实用贝叶斯系统识别
Practical Bayesian System Identification using Hamiltonian Monte Carlo
论文作者
论文摘要
本文使用马尔可夫链蒙特卡洛（MCMC）方法考虑了动态系统的贝叶斯参数估计。采用了Metroplis-Hastings（MH）算法，本文的主要贡献是检查和说明基于保留Hamiltonian动态能量的特定提案密度的功效，从而导致统计学文献中已知的``Hamiltonian Monte-Monte-Carlo-Carlo''（HMC）。这种方法的非常重要的效用是，正如将说明的那样，它大大降低了（几乎达到消除的地步），在大都市 - 悬挂链中通常非常高的相关性，几位作者已经观察到，将MH方法限制为仅将MH方法应用于仅维度很低的模型结构。本文说明了如何将HMC方法应用于显着的尺寸线性和非线性模型结构，即使系统顺序未知以及使用模拟和真实数据。
This paper considers Bayesian parameter estimation of dynamic systems using a Markov Chain Monte Carlo (MCMC) approach. The Metroplis-Hastings (MH) algorithm is employed, and the main contribution of the paper is to examine and illustrate the efficacy of a particular proposal density based on energy preserving Hamiltonian dynamics, which results in what is known in the statistics literature as ``Hamiltonian Monte--Carlo'' (HMC). The very significant utility of this approach is that, as will be illustrated, it greatly reduces (almost to the point of elimination) the typically very high correlation in the Metropolis--Hastings chain which has been observed by several authors to restrict the application of the MH approach to only very low dimension model structures. The paper illustrates how the HMC approach may be applied to both significant dimension linear and nonlinear model structures, even when the system order is unknown, and using both simulated and real data.
