There are many ways to cleverly slice up GP likelihoods so that inference is cheap. One is the Vecchia approxiamtion: Approximate the precision matrix by one with a sparse cholesky factorisation.
TBD.
References
Banerjee, Sudipto, Alan E. Gelfand, Andrew O. Finley, and Huiyan Sang. 2008. “Gaussian Predictive Process Models for Large Spatial Data Sets.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 70 (4): 825–48.
Datta, Abhirup, Sudipto Banerjee, Andrew O. Finley, and Alan E. Gelfand. 2016. “Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets.” Journal of the American Statistical Association 111 (514): 800–812.
Gramacy, Robert B. 2016. “laGP: Large-Scale Spatial Modeling via Local Approximate Gaussian Processes in R.” Journal of Statistical Software 72 (1).
Gramacy, Robert B., and Daniel W. Apley. 2015. “Local Gaussian Process Approximation for Large Computer Experiments.” Journal of Computational and Graphical Statistics 24 (2): 561–78.
Guinness, Joseph. 2019. “Gaussian Process Learning via Fisher Scoring of Vecchia’s Approximation.” arXiv:1905.08374 [Stat], May.
Khare, Kshitij, and Bala Rajaratnam. 2011. “Wishart Distributions for Decomposable Covariance Graph Models.” The Annals of Statistics 39 (1): 514–55.
Pardo-Igúzquiza, Eulogio. 1998. “Maximum Likelihood Estimation of Spatial Covariance Parameters.” Mathematical Geology 30 (1): 95–108.
Peruzzi, Michele, Sudipto Banerjee, and Andrew O. Finley. 2020. “Highly Scalable Bayesian Geostatistical Modeling via Meshed Gaussian Processes on Partitioned Domains.” Journal of the American Statistical Association 0 (0): 1–14.
Pourahmadi, Mohsen. 2007. “Cholesky Decompositions and Estimation of A Covariance Matrix: Orthogonality of Variance–Correlation Parameters.” Biometrika 94 (4): 1006–13.
Vecchia, A. V. 1988. “Estimation and Model Identification for Continuous Spatial Processes.” Journal of the Royal Statistical Society: Series B (Methodological) 50 (2): 297–312.
Zammit-Mangion, Andrew, Michael Bertolacci, Jenny Fisher, Ann Stavert, Matthew L. Rigby, Yi Cao, and Noel Cressie. 2021. “WOMBAT v1.0: A fully Bayesian global flux-inversion framework.” Geoscientific Model Development Discussions, July, 1–51.
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