deepgp: Bayesian Deep Gaussian Processes using MCMC

Performs Bayesian posterior inference for deep Gaussian processes following Sauer, Gramacy, and Higdon (2023, <doi:10.48550/arXiv.2012.08015>). See Sauer (2023, <http://hdl.handle.net/10919/114845>) for comprehensive methodological details and <https://bitbucket.org/gramacylab/deepgp-ex/> for a variety of coding examples. Models are trained through MCMC including elliptical slice sampling of latent Gaussian layers and Metropolis-Hastings sampling of kernel hyperparameters. Gradient-enhancement and gradient predictions are offered following Booth (2025, <doi:10.48550/arXiv.2512.18066>). Vecchia approximation for faster computation is implemented following Sauer, Cooper, and Gramacy (2023, <doi:10.48550/arXiv.2204.02904>). Optional monotonic warpings are implemented following Barnett et al. (2025, <doi:10.48550/arXiv.2408.01540>). Downstream tasks include sequential design through active learning Cohn/integrated mean squared error (ALC/IMSE; Sauer, Gramacy, and Higdon, 2023), optimization through expected improvement (EI; Gramacy, Sauer, and Wycoff, 2022, <doi:10.48550/arXiv.2112.07457>), and contour location through entropy (Booth, Renganathan, and Gramacy, 2025, <doi:10.48550/arXiv.2308.04420>). Models extend up to three layers deep; a one layer model is equivalent to typical Gaussian process regression. Incorporates OpenMP and SNOW parallelization and utilizes C/C++ under the hood.

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