论文标题
利用哈密顿方程的新时空模型
A New Spatio-Temporal Model Exploiting Hamiltonian Equations
论文作者
论文摘要
已知汉密尔顿方程的溶液描述了机械系统的基本相空间。在本文中，我们提出了一种新型的时空模型，该模型使用哈密顿方程的策略修改，通过高斯过程结合了适当的随机性。随着时间的流逝，随之而来的时空过程被证明是非参数，非平稳，不可分割的和非高斯的。另外，随着时空滞后为无限，滞后的相关性会趋于零。我们研究了新时空过程的理论特性，包括其连续性和平滑度。我们得出了使用贝叶斯范式中使用MCMC技术的完整贝叶斯推理的方法。使用两项模拟研究将我们方法的性能与非平稳性高斯工艺（GP）的性能进行了比较，在该研究中，我们的方法对非平稳的GP表现出显着改善。此外，将我们的新模型应用于两个真实数据集，揭示了令人鼓舞的性能。
The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations, incorporating appropriate stochasticity via Gaussian processes. The resultant spatio-temporal process, continuously varying with time, turns out to be nonparametric, non-stationary, non-separable, and non-Gaussian. Additionally, the lagged correlations converge to zero as the spatio-temporal lag goes to infinity. We investigate the theoretical properties of the new spatio-temporal process, including its continuity and smoothness properties. We derive methods for complete Bayesian inference using MCMC techniques in the Bayesian paradigm. The performance of our method has been compared with that of a non-stationary Gaussian process (GP) using two simulation studies, where our method shows a significant improvement over the non-stationary GP. Further, applying our new model to two real data sets revealed encouraging performance.
