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规则网格上 Matérn 协方差的逆AI 解读

Summary We conduct a study of the aliased spectral densities of Matérn covariance functions on a regular grid of points, elucidating the properties of a popular approximation based on stochastic partial differential equations. While other researchers have shown that this approximation can work well for the covariance function, we find that it assigns too much power at high frequencies and does not provide increasingly accurate approximations to the inverse as the grid…

通过周期嵌入估计随机场的谱密度AI 解读

We introduce methods for estimating the spectral density of a random field on a $d$-dimensional lattice from incomplete gridded data. Data are iteratively imputed onto an expanded lattice according to a model with a periodic covariance function. The imputations are convenient computationally, in that circulant embedding and preconditioned conjugate gradient methods can produce imputations in $O(n\log n)$ time and $O(n)$ memory. However, these so-called periodic imputations…

气候模型输出的压缩与条件模拟AI 解读

Numerical climate model simulations run at high spatial and temporal resolutions generate massive quantities of data. As our computing capabilities continue to increase, storing all of the data is not sustainable, and thus it is important to develop methods for representing the full datasets by smaller compressed versions. We propose a statistical compression and decompression algorithm based on storing a set of summary statistics as well as a statistical model describing…

气候变化下基于空间模型的最优种源配置：美国东南部火炬松应用AI 解读

Provenance tests are a common tool in forestry designed to identify superior genotypes for planting at specific locations. The trials are replicated experiments established with seed from parent trees collected from different regions and grown at several locations. In this work, a Bayesian spatial approach is developed for modeling the expected relative performance of seed sources using climate variables as predictors associated with the origin of seed source and the…