A 2-dimensional data set that can be used to validate non-stationary models.
data(exp2d)A data frame with 441 observations on the following 4 variables.
X1Numeric vector describing the first dimension of X inputs
X2Numeric vector describing the second dimension of X inputs
ZNumeric vector describing the response Z(X)+N(0,sd=0.001)
ZtrueNumeric vector describing the true response Z(X),
without noise
Robert B. Gramacy, rbg@vt.edu, and Matt Taddy, mataddy@amazon.com
The true response is evaluated as
$$Z(X)=x_1 * \exp(x_1^2-x_2^2).$$
Zero-mean normal noise
with sd=0.001 has been added to the true response
Gramacy, R. B. (2020) Surrogates: Gaussian Process Modeling, Design and Optimization for the Applied Sciences. Boca Raton, Florida: Chapman Hall/CRC. https://bobby.gramacy.com/surrogates/
Gramacy, R. B. (2007). tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models. Journal of Statistical Software, 19(9). https://www.jstatsoft.org/v19/i09 tools:::Rd_expr_doi("10.18637/jss.v019.i09")
Robert B. Gramacy, Matthew Taddy (2010). Categorical Inputs, Sensitivity Analysis, Optimization and Importance Tempering with tgp Version 2, an R Package for Treed Gaussian Process Models. Journal of Statistical Software, 33(6), 1--48. https://www.jstatsoft.org/v33/i06/. tools:::Rd_expr_doi("10.18637/jss.v033.i06")
Gramacy, R. B., Lee, H. K. H. (2008). Bayesian treed Gaussian process models with an application to computer modeling. Journal of the American Statistical Association, 103(483), pp. 1119-1130. Also available as ArXiv article 0710.4536 https://arxiv.org/abs/0710.4536
exp2d.rand, exp2d.Z,
btgp, and other b* functions