tgp (version 2.4-23)

exp2d.Z: Random Z-values for 2-d Exponential Data

Description

Evaluate the functional (mean) response for the 2-d exponential data (truth) at the X inputs, and randomly sample noisy Z--values having normal error with standard deviation provided.

Usage

exp2d.Z(X, sd=0.001)

Value

Output is a data.frame with columns:

Z

Numeric vector describing the responses (with noise) at the X input locations

Ztrue

Numeric vector describing the true responses (without noise) at the X input locations

Arguments

X

Must be a matrix or a data.frame with two columns describing input locations

sd

Standard deviation of iid normal noise added to the responses

Author

Robert B. Gramacy, , and Matt Taddy,

Details

The response is evaluated as $$Z(X)=x_1 * \exp(x_1^2-x_2^2).$$ thus creating the outputs Z and Ztrue. Zero-mean normal noise with sd=0.001 is added to the responses Z and ZZ

References

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

https://bobby.gramacy.com/r_packages/tgp/

See Also

exp2d, exp2d.rand

Examples

N <- 20
x <- seq(-2,6,length=N)
X <- expand.grid(x, x)
Zdata <- exp2d.Z(X)
persp(x,x,matrix(Zdata$Ztrue, nrow=N), theta=-30, phi=20,
      main="Z true", xlab="x1", ylab="x2", zlab="Ztrue")