论文标题
固定和非组织过程的最佳自适应贝叶斯光谱密度估计
Optimally adaptive Bayesian spectral density estimation for stationary and nonstationary processes
论文作者
论文摘要
本文改进了现有的方法，以估计固定时间和非组织时间序列的光谱密度，并假定先前是高斯过程。通过使用平滑样条协方差结构来优化适当的特征分类，我们的方法更适当地模拟具有简单和复杂的周期性结构的数据。我们通过研究平滑样条以外的其他协方差函数的性能，进一步证明了这种最佳特征分类的实用性。我们表明，最佳特征组件可提供材料的改进，而在检查中的其他协方差功能却没有相对均与平滑样条相对均能表现良好。在计算研究中，我们介绍了来自物理科学启发的光谱密度估算的新验证指标。我们在广泛的仿真研究中验证了我们的模型，并通过实际数据证明了卓越的性能。
This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance structure, our method more appropriately models data with both simple and complex periodic structure. We further justify the utility of this optimal eigendecomposition by investigating the performance of alternative covariance functions other than smoothing splines. We show that the optimal eigendecomposition provides a material improvement, while the other covariance functions under examination do not, all performing comparatively well as the smoothing spline. During our computational investigation, we introduce new validation metrics for the spectral density estimate, inspired from the physical sciences. We validate our models in an extensive simulation study and demonstrate superior performance with real data.
