GPBayes - Tools for Gaussian Process Modeling in Uncertainty
Quantification
Gaussian processes ('GPs') have been widely used to model
spatial data, 'spatio'-temporal data, and computer experiments
in diverse areas of statistics including spatial statistics,
'spatio'-temporal statistics, uncertainty quantification, and
machine learning. This package creates basic tools for fitting
and prediction based on 'GPs' with spatial data,
'spatio'-temporal data, and computer experiments. Key
characteristics for this GP tool include: (1) the comprehensive
implementation of various covariance functions including the
'Matérn' family and the Confluent 'Hypergeometric' family with
isotropic form, tensor form, and automatic relevance
determination form, where the isotropic form is widely used in
spatial statistics, the tensor form is widely used in design
and analysis of computer experiments and uncertainty
quantification, and the automatic relevance determination form
is widely used in machine learning; (2) implementations via
Markov chain Monte Carlo ('MCMC') algorithms and optimization
algorithms for GP models with all the implemented covariance
functions. The methods for fitting and prediction are mainly
implemented in a Bayesian framework; (3) model evaluation via
Fisher information and predictive metrics such as predictive
scores; (4) built-in functionality for simulating 'GPs' with
all the implemented covariance functions; (5) unified
implementation to allow easy specification of various 'GPs'.
