Vecchia Approximations of Gaussian-Process Predictions

Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2004). Hierarchical Modeling and Analysis for Spatial Data. Chapman & Hall, Boca Raton.

Banerjee, S., Gelfand, A. E., Finley, A. O., and Sang, H. (2008). Gaussian predictive process models for large spatial data sets. Journal of the Royal Statistical Society, Series B, 70(4):825–848.

Cressie, N. and Johannesson, G. (2008). Fixed rank kriging for very large spatial data sets. Journal of the Royal Statistical Society, Series B, 70(1):209–226.

Cressie, N. and Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. Wiley, Hoboken, NJ.

Curriero, F. C. and Lele, S. (1999). A composite likelihood approach to semivariogram estimation. Journal of Agricultural, Biological, and Environmental Statistics, 4(1):9–28.

Datta, A., Banerjee, S., Finley, A. O., and Gelfand, A. E. (2016). Hierarchical nearest-neighbor Gaussian process models for large geostatistical datasets. Journal of the American Statistical Association, 111(514):800–812.

Du, J., Zhang, H., and Mandrekar, V. S. (2009). Fixed-domain asymptotic properties of tapered maximum likelihood estimators. The Annals of Statistics, 37:3330–3361.

Eidsvik, J., Shaby, B. A., Reich, B. J., Wheeler, M., and Niemi, J. (2014). Estimation and prediction in spatial models with block composite likelihoods using parallel computing. Journal of Computational and Graphical Statistics, 23(2):295–315.

Erisman, A. M. and Tinney, W. F. (1975). On computing certain elements of the inverse of a sparse matrix. Communications of the ACM, 18(3):177–179.

Finley, A. O., Datta, A., Cook, B. C., Morton, D. C., Andersen, H. E., and Banerjee, S. (2019). Efficient algorithms for Bayesian nearest neighbor Gaussian processes. Journal of Computational and Graphical Statistics, 28(2):401–414.

Finley, A. O., Sang, H., Banerjee, S., and Gelfand, A. E. (2009). Improving the performance of predictive process modeling for large datasets. Computational Statistics & Data Analysis, 53(8):2873–2884.

Foreman-Mackey, D., Agol, E., Ambikasaran, S., and Angus, R. (2017). Fast and scalable Gaussian process modeling with applications to astronomical time series. The Astronomical Journal, 154:220.

Furrer, R., Genton, M. G., and Nychka, D. (2006). Covariance tapering for interpolation of large spatial datasets. Journal of Computational and Graphical Statistics, 15(3):502–523.

Gneiting, T. and Katzfuss, M. (2014). Probabilistic forecasting. Annual Review of Statistics and Its Application, 1(1):125–151.

Gramacy, R. B. and Apley, D. W. (2015). Local Gaussian process approximation for large computer experiments. Journal of Computational and Graphical Statistics, 24(2):561–578.

Guan, K., Berry, J. A., Zhang, Y., Joiner, J., Guanter, L., Badgley, G., and Lobell, D. B. (2016). Improving the monitoring of crop productivity using spaceborne solar-induced fluorescence. Global Change Biology, 22(2):716–726.

Guinness, J. (2018). Permutation methods for sharpening Gaussian process approximations. Technometrics, 60(4):415–429.

Guinness, J. (2019). Spectral density estimation for random fields via periodic embeddings. Biometrika, 106(2):267–286.

Heaton, M. J., Datta, A., Finley, A. O., Furrer, R., Guinness, J., Guhaniyogi, R., Gerber, F., Gramacy, R. B., Hammerling, D., Katzfuss, M., Lindgren, F., Nychka, D. W., Sun, F., and Zammit-Mangion, A. (2019). A case study competition among methods for analyzing large spatial data. Journal of Agricultural, Biological, and Environmental Statistics, 24(3):398–425.

Higdon, D. (1998). A process-convolution approach to modelling temperatures in the North Atlantic Ocean. Environmental and Ecological Statistics, 5(2):173–190.

Jones, D. R., Schonlau, M., and W. J. Welch (1998). Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13:455–492.

Jurek, M. and Katzfuss, M. (2018). Multi-resolution filters for massive spatio-temporal data. arXiv:1810.04200.

Katzfuss, M. (2017). A multi-resolution approximation for massive spatial datasets. Journal of the American Statistical Association, 112(517):201–214.

Katzfuss, M. and Cressie, N. (2011). Spatio-temporal smoothing and EM estimation for massive remote-sensing data sets. Journal of Time Series Analysis, 32(4):430–446.

Katzfuss, M. and Gong, W. (2019). A class of multi-resolution approximations for large spatial datasets. Statistica Sinica. https://doi.org/10.5705/ss.202018.0285.

Katzfuss, M. and Guinness, J. (2019). A general framework for Vecchia approximations of Gaussian processes. Statistical Science, accepted.

Katzfuss, M., Guinness, J., and Lawrence, E. (2020a). Scaled Vecchia approximation for fast computer-model emulation. arXiv:2005.00386.

Katzfuss, M., Jurek, M., Zilber, D., Gong, W., Guinness, J., Zhang, J., and Schäfer, F. (2020b). GPvecchia: Fast Gaussian-process inference using Vecchia approximations. R package version 0.1.3.

Kaufman, C. G., Schervish, M. J., and Nychka, D. W. (2008). Covariance tapering for likelihood-based estimation in large spatial data sets. Journal of the American Statistical Association, 103(484):1545–1555.

Kelly, B. C., Becker, A. C., Sobolewska, M., Siemiginowska, A., and Uttley, P. (2014). Flexible and scalable methods for quantifying stochastic variability in the era of massive time-domain astronomical data sets. Astrophysical Journal, 788(1):33.

Kennedy, M. C. and O’Hagan, A. (2001). Bayesian calibration of computer models. Journal of the Royal Statistical Society: Series B, 63(3):425–464.

Le, N. D. and Zidek, J. V. (2006). Statistical Analysis of Environmental Space-Time Processes. Springer, Berlin.

Li, S., Ahmed, S., Klimeck, G., and Darve, E. (2008). Computing entries of the inverse of a sparse matrix using the FIND algorithm. Journal of Computational Physics, 227(22):9408–9427.

Lin, L., Yang, C., Meza, J., Lu, J., Ying, L., and Weinan, E. (2011). SelInv—An algorithm for selected inversion of a sparse symmetric matrix. ACM Transactions on Mathematical Software, 37(4):40.

Lindgren, F., Rue, H., and Lindström, J. (2011). An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. Journal of the Royal Statistical Society: Series B, 73(4):423–498.

Nychka, D. W., Bandyopadhyay, S., Hammerling, D., Lindgren, F., and Sain, S. R. (2015). A multi-resolution Gaussian process model for the analysis of large spatial data sets. Journal of Computational and Graphical Statistics, 24(2):579–599.

OCO-2 Science Team, Gunson, M., and Eldering, A. (2015). OCO-2 Level 2 bias-corrected solar-induced fluorescence and other select fields from the IMAP-DOAS algorithm aggregated as daily files, retrospective processing V7r. https://disc.gsfc.nasa.gov/datacollection/OCO2_L2_Lite_SIF_7r.html

Quiñonero-Candela, J. and Rasmussen, C. E. (2005). A unifying view of sparse approximate Gaussian process regression. Journal of Machine Learning Research, 6:1939–1959.

Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press, Cambridge.

Rue, H. and Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications. CRC Press, Boca Raton.

Sang, H., Jun, M., and Huang, J. Z. (2011). Covariance approximation for large multivariate spatial datasets with an application to multiple climate model errors. Annals of Applied Statistics, 5(4):2519–2548.

Schäfer, F., Katzfuss, M., and Owhadi, H. (2020). Sparse Cholesky factorization by Kullback–Leibler minimization. arXiv:2004.14455.

Schäfer, F., Sullivan, T. J., and Owhadi, H. (2017). Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity. arXiv:1706.02205.

Snelson, E. and Ghahramani, Z. (2007). Local and global sparse Gaussian process approximations. In Artificial Intelligence and Statistics 11 (AISTATS).

Snoek, J., Larochelle, H., and Adams, R. P. (2012). Practical Bayesian optimization of machine learning algorithms. In Neural Information Processing Systems.

Stein, M. L., Chi, Z., and Welty, L. (2004). Approximating likelihoods for large spatial data sets. Journal of the Royal Statistical Society: Series B, 66(2):275–296.

Stroud, J. R., Stein, M. L., and Lysen, S. (2017). Bayesian and maximum likelihood estimation for Gaussian processes on an incomplete lattice. Journal of Computational and Graphical Statistics, 26(1):108–120.

Sun, Y., Frankenberg, C., Jung, M., Joiner, J., Guanter, L., Köhler, P., and Magney, T. (2018). Overview of solar-induced chlorophyll fluorescence (sif) from the orbiting carbon observatory-2: Retrieval, cross-mission comparison, and global monitoring for gpp. Remote Sensing of Environment, 209:808–823.

Sun, Y., Frankenberg, C., Wood, J. D., Schimel, D. S., Jung, M., Guanter, L., Drewry, D., Verma, M., Porcar-Castell, A., Griffis, T. J., et al. (2017). Oco-2 advances photosynthesis observation from space via solar-induced chlorophyll fluorescence. Science, 358(6360):eaam5747.

Sun, Y. and Stein, M. L. (2016). Statistically and computationally efficient estimating equations for large spatial datasets. Journal of Computational and Graphical Statistics, 25(1):187–208.

Tzeng, S. and Huang, H.-C. (2018). Resolution adaptive fixed rank kriging. Technometrics, 60(2):198–208.

Vecchia, A. (1988). Estimation and model identification for continuous spatial processes. Journal of the Royal Statistical Society, Series B, 50(2):297–312.

Vecchia, A. (1992). A new method of prediction for spatial regression models with correlated errors. Journal of the Royal Statistical Society, Series B, 54(3):813–830.

Wang, Y., Khardon, R., and Protopapas, P. (2012). Nonparametric Bayesian estimation of periodic light curves. Astrophysical Journal, 756(1):67.

Wikle, C. K. and Cressie, N. (1999). A dimension-reduced approach to space-time Kalman filtering. Biometrika, 86(4):815–829.

Zhang, B., Sang, H., and Huang, J. Z. (2019). Smoothed full-scale approximation of Gaussian process models for computation of large spatial datasets. Statistica Sinica, 29:1711–1737.

Zilber, D. and Katzfuss, M. (2019). Vecchia-Laplace approximations of generalized Gaussian processes for big non-Gaussian spatial data. arXiv:1906.07828.