README.md

In maatouk/constrKriging: Kriging with inequality constraints

output: html_document

Kriging with inequality constraints for computer experiments

This repository contains an R Package to build, simulate, predict kriging model using inequality constraints such as boundedness, monotonicity and convexity. Kriging model is similar to DiceKriging.

Installation

You can install the latest version of the code using the devtools R package.

# Install devtools, if you haven't already.
install.packages("devtools")

library(devtools)
install_github("maatouk/constrKriging")

Usage

## Golchi Example
f <- function(x){
log(20*x+1)
}

design <- c(0, 0.1, 0.2, 0.3, 0.4, 0.9, 1)
response <- f(design)

meany <- mean(response)
f <- function(x){
log(20*x+1)-meany
}

design <- c(0, 0.1, 0.2, 0.3, 0.4, 0.9, 1)
response <- f(design)

model = kmMonotonic1D(design, response, covtype="matern5_2", basis.size=50, coef.var=355^2, coef.cov=4.37, nugget=1e-7)

plot(f, ylab='response', xlab='design')

plot(object=model, spline=TRUE, quantiles=TRUE, col='gray',nsim=1000, add=T)

points(design,response,pch=19)

legend(0.2,-0.5, c("true function","posterior max","constrained 95% intervals"),
col = c('black','gray','gray'), text.col = "black",
lty = c(1, 1, 1), pch=c(NA_integer_, NA_integer_),
lwd = c(2, 2, 10), text.font=1,box.lty=0)

References

Maatouk, H. and Bay, X. (2017). Gaussian Process Emulators for Computer Experiments with Inequality Constraints. Mathematical Geosciences 49(5):557–582

Cousin, A., Maatouk, H. and Rullière, D. (2016). Kriging of Financial Term-Structures. European Journal of Operational Research 255(2):631–648

Bay X., Grammont, L. and Maatouk, H. (2016). Generalization of the Kimeldorf-Wahba Correspondence for Constrained Interpolation. Electronic Journal of Statistics 10(1):1580–1595

Maatouk, H. and Bay, X. (2014). A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets. In: Nuyens R, Cools R (ed) Monte Carlo and Quasi-Monte Carlo Methods, vol 163. Springer International Publishing, Cham, pp 521–530

Maatouk, H., Roustant, O., and Richet, Y. (2015). Cross-Validation Estimations of Hyper-Parameters of Gaussian Processes with Inequality Constraints. Procedia Environmental Sciences, 27:38–44, 2015. Spatial Statistics conference 2015

Bay, X., Grammont, L., and Maatouk, H. (2017). A New Method For Interpolating In A Convex Subset Of A Hilbert Space. Computational Optimization and Applications 68(1):95-120

maatouk/constrKriging documentation built on May 21, 2019, 10:50 a.m.