702 research outputs found

    Categorical Inputs, Sensitivity Analysis, Optimization and Importance Tempering with tgp Version 2, an R Package for Treed Gaussian Process Models

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    This document describes the new features in version 2.x of the tgp package for R, implementing treed Gaussian process (GP) models. The topics covered include methods for dealing with categorical inputs and excluding inputs from the tree or GP part of the model; fully Bayesian sensitivity analysis for inputs/covariates; sequential optimization of black-box functions; and a new Monte Carlo method for inference in multi-modal posterior distributions that combines simulated tempering and importance sampling. These additions extend the functionality of tgp across all models in the hierarchy: from Bayesian linear models, to classification and regression trees (CART), to treed Gaussian processes with jumps to the limiting linear model. It is assumed that the reader is familiar with the baseline functionality of the package, outlined in the first vignette (Gramacy 2007).

    tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models

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    The tgp package for R is a tool for fully Bayesian nonstationary, semiparametric nonlinear regression and design by treed Gaussian processes with jumps to the limiting linear model. Special cases also implemented include Bayesian linear models, linear CART, stationary separable and isotropic Gaussian processes. In addition to inference and posterior prediction, the package supports the (sequential) design of experiments under these models paired with several objective criteria. 1-d and 2-d plotting, with higher dimension projection and slice capabilities, and tree drawing functions (requiring maptree and combinat packages), are also provided for visualization of tgp objects.

    Categorical Inputs, Sensitivity Analysis, Optimization and Importance Tempering with tgp Version 2, an R Package for Treed Gaussian Process Models

    Get PDF
    This document describes the new features in version 2.x of the tgp package for R, implementing treed Gaussian process (GP) models. The topics covered include methods for dealing with categorical inputs and excluding inputs from the tree or GP part of the model; fully Bayesian sensitivity analysis for inputs/covariates; sequential optimization of black-box functions; and a new Monte Carlo method for inference in multi-modal posterior distributions that combines simulated tempering and importance sampling. These additions extend the functionality of tgp across all models in the hierarchy: from Bayesian linear models, to classification and regression trees (CART), to treed Gaussian processes with jumps to the limiting linear model. It is assumed that the reader is familiar with the baseline functionality of the package, outlined in the first vignette (Gramacy 2007)

    Gaussian process single-index models as emulators for computer experiments

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    A single-index model (SIM) provides for parsimonious multi-dimensional nonlinear regression by combining parametric (linear) projection with univariate nonparametric (non-linear) regression models. We show that a particular Gaussian process (GP) formulation is simple to work with and ideal as an emulator for some types of computer experiment as it can outperform the canonical separable GP regression model commonly used in this setting. Our contribution focuses on drastically simplifying, re-interpreting, and then generalizing a recently proposed fully Bayesian GP-SIM combination, and then illustrating its favorable performance on synthetic data and a real-data computer experiment. Two R packages, both released on CRAN, have been augmented to facilitate inference under our proposed model(s).Comment: 23 pages, 9 figures, 1 tabl
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