论文标题
使用随机微分方程对非均匀采样时间序列的准确表征
Accurate Characterization of Non-Uniformly Sampled Time Series using Stochastic Differential Equations
论文作者
论文摘要
当实验者无法完全控制所研究过程的采样特征时，就会出现不均匀的采样。此外，它是在贝叶斯优化和压缩传感等算法中有意引入的。我们认为随机微分方程（SDE）特别适合表征此类时间序列的二阶时刻。我们基于自回旋模型的增量估计和初始化，为可能性的数值优化介绍了新的初始估计。此外，我们将模型截断引入了一种纯粹的数据驱动方法，以减少基于SDE可能性的估计模型的顺序。我们表明，在模拟实验中，新的估计量提高了精度，涵盖了表征不均匀采样时间序列时可能遇到的所有具有挑战性的情况。最后，我们将新估计量应用于实验降雨可变性数据。
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and compressive sensing. We argue that Stochastic Differential Equations (SDEs) are especially well-suited for characterizing second order moments of such time series. We introduce new initial estimates for the numerical optimization of the likelihood, based on incremental estimation and initialization from autoregressive models. Furthermore, we introduce model truncation as a purely data-driven method to reduce the order of the estimated model based on the SDE likelihood. We show the increased accuracy achieved with the new estimator in simulation experiments, covering all challenging circumstances that may be encountered in characterizing a non-uniformly sampled time series. Finally, we apply the new estimator to experimental rainfall variability data.
