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  "Title": "Bayesian Deep Gaussian Processes using MCMC",
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  "Date": "2026-02-06",
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  "Description": "Performs Bayesian posterior inference for deep Gaussian\nprocesses following Sauer, Gramacy, and Higdon (2023,\n<doi:10.48550/arXiv.2012.08015>). See Sauer (2023,\n<http://hdl.handle.net/10919/114845>) for comprehensive\nmethodological details and\n<https://bitbucket.org/gramacylab/deepgp-ex/> for a variety of\ncoding examples. Models are trained through MCMC including\nelliptical slice sampling of latent Gaussian layers and\nMetropolis-Hastings sampling of kernel hyperparameters.\nGradient-enhancement and gradient predictions are offered\nfollowing Booth (2025, <doi:10.48550/arXiv.2512.18066>).\nVecchia approximation for faster computation is implemented\nfollowing Sauer, Cooper, and Gramacy (2023,\n<doi:10.48550/arXiv.2204.02904>).  Optional monotonic warpings\nare implemented following Barnett et al. (2025,\n<doi:10.48550/arXiv.2408.01540>). Downstream tasks include\nsequential design through active learning Cohn/integrated mean\nsquared error (ALC/IMSE; Sauer, Gramacy, and Higdon, 2023),\noptimization through expected improvement (EI; Gramacy, Sauer,\nand Wycoff, 2022, <doi:10.48550/arXiv.2112.07457>), and contour\nlocation through entropy (Booth, Renganathan, and Gramacy,\n2025, <doi:10.48550/arXiv.2308.04420>).  Models extend up to\nthree layers deep; a one layer model is equivalent to typical\nGaussian process regression. Incorporates OpenMP and SNOW\nparallelization and utilizes C/C++ under the hood.",
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