2020/12/10 by Brian Kidd, Kidd, Brian, Matthias Katzfuß +1 · 1 citation
Economics, Econometrics and Finance · Environmental Science · Mathematics · #Applications (stat.AP) #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Soil Geostatistics and Mapping #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2012.05967
openalex publication_date 2020/12/10 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In spatial statistics, it is often assumed that the spatial field of interest\nis stationary and its covariance has a simple parametric form, but these\nassumptions are not appropriate in many applications. Given replicate\nobservations of a Gaussian spatial field, we propose nonstationary and\nnonparametric Bayesian inference on the spatial dependence. Instead of\nestimating the quadratic (in the number of spatial locations) entries of the\ncovariance matrix, the idea is to infer a near-linear number of nonzero entries\nin a sparse Cholesky factor of the precision matrix. Our prior assumptions are\nmotivated by recent results on the exponential decay of the entries of this\nCholesky factor for Matern-type covariances under a specific ordering scheme.\nOur methods are highly scalable and parallelizable. We conduct numerical\ncomparisons and apply our methodology to climate-model output, enabling\nstatistical emulation of an expensive physical model.\n