Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present a novel approximate inference methodology that uses profile likelihood and Krylov subspace methods to estimate the spatial covariance parameters and makes spatial predictions with uncertainty quantification. The proposed method, Kryging, applies for both observations on regular grid and irregularly-spaced observations, and for any Gaussian process with a stationary covariance function, including the popular $\Matern$ covariance family. We make use of the block Toeplitz structure with Toeplitz blocks of the covariance matrix and use fast Fourier transform methods to alleviate the computational and memory bottlenecks. We perform extensive simulation studies to show the effectiveness of our model by varying sample sizes, spatial parameter values and sampling designs. A real data application is also performed on a dataset consisting of land surface temperature readings taken by the MODIS satellite. Compared to existing methods, the proposed method performs satisfactorily with much less computation time and better scalability.
翻译:使用高斯进程模型分析大规模空间数据集给计算带来挑战,这是环境建模、生态、林业和环境热量等应用中普遍存在的一个问题。我们提出了一个新颖的近似推导方法,使用剖析概率和Krylov子空间方法估计空间共变参数,并用不确定的量化方法进行空间预测。拟议的方法Kryging既适用于常规网格和不定期间距观测的观测,也适用于具有固定性共变函数的高斯进程,包括流行的美元和元共变数家庭。我们使用与共变矩阵托普利茨区块的块块块块的托普利茨结构,并使用快速四倍变法减轻计算和记忆瓶颈。我们进行了广泛的模拟研究,以不同样本大小、空间参数值和取样设计来显示我们模型的有效性。还在由MODIS卫星测得的地面温度读数组成的数据集上进行了实际数据应用。与现有方法相比,拟议方法的计算结果令人满意,以更精确的时间和更精确的缩度。