[28] KNAPIK, B. T., VAN DER VAART, A. W., AND VAN ZANTEN, J. H. Bayesian recovery of the initial condition for the heat equation. Communications in Statistics-Theory and Methods 42, 7 (2013), 1294-1313.
[29] LAW, K., STUART, A., AND ZYGALAKIS, K. Data assimilation. Cham, Switzerland: Springer 214 (2015), 52.
[30] LÁZARO-GREDILLA, M., AND FIGUEIRAS-VIDAL, A. Inter-domain gaussian processes for sparse inference using inducing features. In Advances in Neural Information Processing Systems (2009), Y. Bengio, D. Schuurmans, J. Lafferty, C. Williams, and A. Culotta, Eds., vol. 22, Curran Associates, Inc.
[31] MAESTRINI, L., AYKROYD, R. G., AND WAND, M. P. A variational inference framework for inverse problems. arXiv preprint arXiv:2103.05909 (2021).
[32] MAIR, B. A., AND RUYMGAART, F. H. Statistical inverse estimation in hilbert scales. SIAM Journal on Applied Mathematics 56, 5 (1996), 1424-1444.
[33] MATTHEws, A. G. D. G., HenssMan, J., TURner, R., AND GHAHRAMANI, Z. On sparse variational methods and the kullback-leibler divergence between stochastic processes. In Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (Cadiz, Spain, 09-11 May 2016), A. Gretton and C. C. Robert, Eds., vol. 51 of Proceedings of Machine Learning Research, PMLR, pp. 231-239.
[34] MENG, R., AND YANG, X. Sparse gaussian processes for solving nonlinear pdes. arXiv preprint arXiv:2205.03760 (2022).
[35] NASHED, M. Z., AND WAHBA, G. Generalized inverses in reproducing kernel spaces: An approach to regularization of linear operator equations. SIAM Journal on Mathematical Analysis 5, 6 (1974), 974-987.
[36] NICKL, R. Bayesian non-linear statistical inverse problems. Lecture Notes ETH Zurich (2022).
[37] NiEMAN, D., SZABO, B., AND VAN ZANTEN, H. Contraction rates for sparse variational approximations in gaussian process regression. Journal of Machine Learning Research 23, 205 (2022), 1-26.
[38] NiEMAN, D., SZABO, B., AND VAN ZANTEN, H. Uncertainty quantification for sparse spectral variational approximations in gaussian process regression. arXiv preprint arXiv:2212.11031 (2022).
[39] PATI, D., BHATTACHARYA, A., AND CHENG, G. Optimal Bayesian estimation in random covariate design with a rescaled Gaussian process prior. J. Mach. Learn. Res. 16 (2015), 2837-2851.
[40] PINSKI, F. J., SIMPSON, G., STUART, A. M., AND WEBER, H. Algorithms for kullback–leibler approximation of probability measures in infinite dimensions. SIAM Journal on Scientific Computing 37, 6 (2015), A2733–A2757.
[41] PINSKI, F. J., SIMPSON, G., STUART, A. M., AND WEBER, H. Kullback–leibler approximation for probability measures on infinite dimensional spaces. SIAM Journal on Mathematical Analysis 47, 6 (2015), 4091–4122.
[42] POVALA, J., KAZLAUSKAITE, I., FEBRIANTO, E., CIRAK, F., AND GIROLAMI, M. Variational bayesian approximation of inverse problems using sparse precision matrices. Computer Methods in Applied Mechanics and Engineering 393 (2022), 114712.
[43] QUIÑONERO CANDELA, J., AND RASMUSSEN, C. E. A unifying view of sparse approximate gaussian process regression. J. Mach. Learn. Res. 6 (dec 2005), 1939-1959.
[44] RASMUSSEN, C. E., AND WILLIAMS, C. K. I. Gaussian processes for machine learning. Adaptive Computation and Machine Learning. MIT Press, Cambridge, MA, 2006.
[45] RAY, K. Bayesian inverse problems with non-conjugate priors. Electronic Journal of Statistics 7, none (2013), 2516 - 2549.
[46] RAY, K., AND SZABÓ, B. Variational bayes for high-dimensional linear regression with sparse priors. Journal of the American Statistical Association 117, 539 (2022), 1270-1281.
[47] ROUSSEAU, J., AND SZABO, B. Asymptotic behaviour of the empirical Bayes posteriors associated to maximum marginal likelihood estimator. The Annals of Statistics 45, 2 (2017), 833 - 865.
[48] ROUSSEAU, J., AND SZABO, B. Asymptotic frequentist coverage properties of Bayesian credible sets for sieve priors. The Annals of Statistics 48, 4 (2020), 2155 - 2179.