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# Imported Functions ----------------------------------------------------------
#' @importFrom Matrix t solve
#' @importFrom grDevices heat.colors
#' @importFrom graphics image lines matlines par plot points contour abline
#' @importFrom stats cov dgamma dnorm pnorm qnorm rnorm runif var
#' @importFrom parallel makeCluster detectCores stopCluster
#' @importFrom doParallel registerDoParallel
#' @importFrom foreach %dopar% foreach
#' @importFrom Rcpp sourceCpp
#' @importFrom mvtnorm rmvnorm
#' @importFrom FNN get.knnx
#' @importFrom GpGp find_ordered_nn
# Package Documentation -------------------------------------------------------
#' @useDynLib deepgp, .registration = TRUE
#' @title Package deepgp
#' @author Annie S. Booth \email{annie_booth@ncsu.edu}
#' @docType package
#' @name deepgp-package
#'
#' @description Performs Bayesian posterior inference for deep Gaussian
#' processes following Sauer, Gramacy, and Higdon (2023).
#' See Sauer (2023) for comprehensive
#' methodological details and \url{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. Vecchia-approximation for faster
#' computation is implemented following Sauer, Cooper, and Gramacy
#' (2023). Optional monotonic warpings are implemented following
#' Barnett et al. (2024). 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), and contour
#' location through entropy (Booth, Renganathan, and Gramacy,
#' 2024). 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.
#'
#' @section Important Functions:
#' \itemize{
#' \item \code{\link[deepgp]{fit_one_layer}}: conducts MCMC sampling of
#' hyperparameters for a one layer GP
#' \item \code{\link[deepgp]{fit_two_layer}}: conducts MCMC sampling of
#' hyperparameters and hidden layer for a two layer deep GP
#' \item \code{\link[deepgp]{fit_three_layer}}: conducts MCMC sampling of
#' hyperparameters and hidden layers for a three layer deep GP
#' \item \code{\link[deepgp]{continue}}: collects additional MCMC samples
#' \item \code{\link[deepgp]{trim}}: cuts off burn-in and optionally thins
#' samples
#' \item \code{\link[deepgp]{predict}}: calculates posterior mean and
#' variance over a set of input locations (optionally calculates EI or entropy)
#' \item \code{\link[deepgp]{plot}}: produces trace plots, hidden layer
#' plots, and posterior predictive plots
#' \item \code{\link[deepgp]{ALC}}: calculates active learning Cohn over
#' set of input locations using reference grid
#' \item \code{\link[deepgp]{IMSE}}: calculates integrated mean-squared error
#' over set of input locations
#' }
#'
#' @references
#' Sauer, A. (2023). Deep Gaussian process surrogates for computer experiments.
#' *Ph.D. Dissertation, Department of Statistics, Virginia Polytechnic Institute and State University.*
#' \url{http://hdl.handle.net/10919/114845}
#' \cr\cr
#' Sauer, A., Gramacy, R.B., & Higdon, D. (2023). Active learning for deep
#' Gaussian process surrogates. *Technometrics, 65,* 4-18. arXiv:2012.08015
#' \cr\cr
#' Sauer, A., Cooper, A., & Gramacy, R. B. (2023). Vecchia-approximated deep Gaussian
#' processes for computer experiments.
#' *Journal of Computational and Graphical Statistics, 32*(3), 824-837. arXiv:2204.02904
#' \cr\cr
#' Gramacy, R. B., Sauer, A. & Wycoff, N. (2022). Triangulation candidates for Bayesian
#' optimization. *Advances in Neural Information Processing Systems (NeurIPS), 35,*
#' 35933-35945. arXiv:2112.07457
#' \cr\cr
#' Booth, A., Renganathan, S. A. & Gramacy, R. B. (2024). Contour location for
#' reliability in airfoil simulation experiments using deep Gaussian
#' processes. *In Review.* arXiv:2308.04420
#'
#' Barnett, S., Beesley, L. J., Booth, A. S., Gramacy, R. B., & Osthus D. (2024).
#' Monotonic warpings for additive and deep Gaussian processes. *In Review.* arXiv:2408.01540
#'
#' @examples
#' # See vignette, ?fit_one_layer, ?fit_two_layer, ?fit_three_layer,
#' # ?ALC, or ?IMSE for examples
#' # Many more examples including real-world computer experiments are available at:
#' # https://bitbucket.org/gramacylab/deepgp-ex/
#'
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