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

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. We propose a Vecchia-Laplace approximation for GGPs, which combines a Laplace approximation to the non-Gaussian likelihood with a computationally efficient Vecchia approximation to the GP, resulting in a simple, general, scalable, and accurate methodology. We provide numerical studies and comparisons on simulated and real spatial data. Our methods are implemented in a freely available R package.

arXiv comment26 pages, 10 figures, code available at https://github.com/katzfuss-group/GPvecchia-Laplace

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Cited by in corpus (6)

• Marginal Inference for Hierarchical Generalized Linear Mixed Models with Patterned Covariance Matrices Using the Laplace Approximation
• Fast expectation-maximization algorithms for spatial generalized linear mixed models
• Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models
• Compositionally-warped additive mixed modeling for a wide variety of non-Gaussian spatial data
• Fully Bayesian inference for spatiotemporal data with the multi-resolution approximation
• Sparse nearest neighbor Cholesky matrices in spatial statistics