Vecchia–Laplace approximations of generalized Gaussian processes for big non-Gaussian spatial data

Daniel Zilber and Matthias Katzfuss

Computational Statistics & Data Analysis, 2021, vol. 153, issue C

Abstract: Generalized Gaussian processes (GGPs) are highly flexible models that combine latent GPs with potentially non-Gaussian likelihoods from the exponential family. GGPs can be used in a variety of settings, including GP classification, nonparametric count regression, modeling non-Gaussian spatial data, and analyzing point patterns. However, inference for GGPs can be analytically intractable, and large datasets pose computational challenges due to the inversion of the GP covariance matrix. A Vecchia–Laplace approximation for GGPs is proposed, which combines a Laplace approximation to the non-Gaussian likelihood with a computationally efficient Vecchia approximation to the GP, resulting in simple, general, scalable, and accurate methodology. Numerical studies and comparisons on simulated and real spatial data are provided. The methods are implemented in a freely available R package.

Keywords: Exponential family; Geostatistics; Kriging; Nearest Neighbor; Sparse inverse Cholesky; Spatial Generalized Linear Mixed Model (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:153:y:2021:i:c:s0167947320301729

DOI: 10.1016/j.csda.2020.107081

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