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Abstract:
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Generalized Gaussian processes (GGPs) are highly flexible models that combine a latent GP with a potentially non-Gaussian likelihood from the exponential family, to perform GP classification and non- Gaussian spatial regression. However, inference for GGPs can be analytically intractable, and large datasets pose computational challenges due to the inversion of the GP covariance matrix. To achieve computational feasibility even for very large spatial datasets, we propose a Vecchia-Laplace approximation for GGPs, which combines a Laplace approximation to the non-Gaussian likelihood with a sparse Vecchia approximation to the GP. We outline the properties of the algorithm, provide numerical studies, and show an application to satellite data.
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