论文标题
在Hellinger距离量化观察到的非高斯数据的模型不确定性
Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance
论文作者
论文摘要
随机波动下的复杂系统的数学模型通常是某些不确定的参数。但是，仍然缺乏具有$α$稳定过程的随机微分方程的量化模型不确定性。在这里，我们提出了一种方法，通过将Hellinger在参数空间上的距离最小化来推断所有不确定的非高斯参数和其他系统参数。 Hellinger距离衡量了相关的非局部fokker-Planck方程的非高斯观测的经验概率密度与解决方案（作为概率密度）之间的相似性。数值实验验证我们的方法对于估计单个和多个参数是可行的。同时，我们找到了估计参数的最佳估计间隔。该方法有助于在非高斯波动下提取统治动态系统模型，例如在Dansgaard-Oeschger事件中突然的气候变化的研究中。
Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an $α$-stable Lévy process is still lacking. Here, we propose an approach to infer all the uncertain non-Gaussian parameters and other system parameters by minimizing the Hellinger distance over the parameter space. The Hellinger distance measures the similarity between an empirical probability density of non-Gaussian observations and a solution (as a probability density) of the associated nonlocal Fokker-Planck equation. Numerical experiments verify that our method is feasible for estimating single and multiple parameters. Meanwhile, we find an optimal estimation interval of the estimated parameters. This method is beneficial for extracting governing dynamical system models under non-Gaussian fluctuations, as in the study of abrupt climate changes in the Dansgaard-Oeschger events.
