Quick Harrison, Banerjee Sudipto, Carlin Bradley P
Division of Heart Disease and Stroke Prevention, NCCDPHP/CDC, Atlanta, Georgia 30341-3717, U.S.A.
Department of Biostatistics, University of California, Los Angeles, California 90095-1772, U.S.A.
Biometrics. 2015 Sep;71(3):575-84. doi: 10.1111/biom.12305. Epub 2015 Apr 20.
Stochastic process models are widely employed for analyzing spatiotemporal datasets in various scientific disciplines including, but not limited to, environmental monitoring, ecological systems, forestry, hydrology, meteorology, and public health. After inferring on a spatiotemporal process for a given dataset, inferential interest may turn to estimating rates of change, or gradients, over space and time. This manuscript develops fully model-based inference on spatiotemporal gradients under continuous space, continuous time settings. Our contribution is to offer, within a flexible spatiotemporal process model setting, a framework to estimate arbitrary directional gradients over space at any given timepoint, temporal derivatives at any given spatial location and, finally, mixed spatiotemporal gradients that reflect rapid change in spatial gradients over time and vice-versa. We achieve such inference without compromising on rich and flexible spatiotemporal process models and use nonseparable covariance structures. We illustrate our methodology using a simulated data example and subsequently apply it to a dataset of daily PM2.5 concentrations in California, where the spatiotemporal gradient process reveals the effects of California's unique topography on pollution and detects the aftermath of a devastating series of wildfires.
随机过程模型被广泛用于分析各科学学科中的时空数据集，包括但不限于环境监测、生态系统、林业、水文、气象和公共卫生。在对给定数据集的时空过程进行推断后，推断兴趣可能转向估计空间和时间上的变化率或梯度。本文稿在连续空间、连续时间设置下，开发了基于完全模型的时空梯度推断方法。我们的贡献在于，在一个灵活的时空过程模型设置中，提供一个框架，用于估计在任何给定时间点上空间的任意方向梯度、在任何给定空间位置的时间导数，以及最终反映空间梯度随时间快速变化及反之亦然的混合时空梯度。我们在不影响丰富且灵活的时空过程模型的情况下实现了这种推断，并使用了不可分离的协方差结构。我们用一个模拟数据示例说明了我们的方法，随后将其应用于加利福尼亚州每日PM2.5浓度的数据集，其中时空梯度过程揭示了加利福尼亚州独特地形对污染的影响，并检测到一系列毁灭性野火的后果。
