• Corpus ID: 207795633

Bayesian nonstationary Gaussian process modeling: the BayesNSGP package for R

@inproceedings{Risser2019BayesianNG,
  title={Bayesian nonstationary Gaussian process modeling: the BayesNSGP package for R},
  author={Mark D. Risser and Daniel Turek},
  year={2019}
}
In spite of the diverse literature on nonstationary Gaussian process modeling, the software for implementing convolution-based methods is extremely limited, particularly for fully Bayesian analysis. To address this gap, here we present the BayesNSGP software package for R that enables off-the-shelf functionality for fully Bayesian, nonstationary Gaussian process modeling. Our approach to nonstationary modeling involves a closed-form, convolution-based covariance function with spatially-varying… 

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References

SHOWING 1-10 OF 58 REFERENCES

Local likelihood estimation for covariance functions with spatially-varying parameters: the convoSPAT package for R

TLDR
A new nonstationary covariance function for spatial Gaussian process models that allows for efficient computing in two ways: first, by representing the spatially-varying parameters via a discrete mixture or "mixture component" model, and second, by estimating the mixture component parameters through a local likelihood approach.

Nonstationary Covariance Functions for Gaussian Process Regression

TLDR
In experiments, the nonstationary GP regression model performs well when the input space is two or three dimensions, outperforming a neural network model and Bayesian free-knot spline models, and competitive with a Bayesian neural network, but is outperformed in one dimension by a state-of-the-art BayesianFree-k not spline model.

Vecchia Approximations of Gaussian-Process Predictions

TLDR
A general Vecchia framework for GP predictions is considered, which contains some novel and some existing special cases, and it is shown that certain choices within the framework can have a strong effect on uncertainty quantification and computational cost, which leads to specific recommendations on which methods are most suitable for various settings.

Regression‐based covariance functions for nonstationary spatial modeling

TLDR
This work proposes a Bayesian model for continuously-indexed spatial data based on a flexible parametric covariance regression structure for a convolution-kernel covariance matrix, and explores properties of the implied model, including a description of the resulting nonstationary covariance function and the interpretational benefits in the kernel parameters.

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

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

Bayesian estimation of semi‐parametric non‐stationary spatial covariance structures

We use the Sampson and Guttorp approach to model the non-stationary correlation function r(x, x′) of a Gaussian spatial process through a bijective space deformation, f, so that in the deformed space

Efficient Estimation of Non-stationary Spatial Covariance Functions with Application to High-resolution Climate Model Emulation

TLDR
This study proposes a new estimation procedure to approximate a class of nonstationary Matérn covariance functions by local-polynomial fitting the covariance parameters, and develops an approach for a fast high-resolution simulation with non stationary features on a small scale.

Bayesian Hierarchical Models With Conjugate Full-Conditional Distributions for Dependent Data From the Natural Exponential Family

TLDR
A Bayesian approach for analyzing (possibly) high-dimensional dependent data that are distributed according to a member from the natural exponential family of distributions is introduced, which is motivated by the Diaconis and Ylvisaker distribution.

Review: Nonstationary Spatial Modeling, with Emphasis on Process Convolution and Covariate-Driven Approaches

TLDR
This review document provides a rigorous and concise description of the existing literature on nonstationary methods, paying particular attention to process convolution (also called kernel smoothing or moving average) approaches.

Spatial Modelling Using a New Class of Nonstationary Covariance Functions.

TLDR
A new class of nonstationary covariance functions for spatial modelling, which includes a non stationary version of the Matérn stationary covariance, in which the differentiability of the spatial surface is controlled by a parameter, freeing one from fixing the differentiable in advance.
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