Random Z-values for 2-d Exponential Data

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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

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exp2d.Z(X, sd=0.001)

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

Details

The response is evaluated as

Z(X) = X1 * exp(-X1^2-X2^2),

thus creating the outputs Z and Ztrue. Zero-mean normal noise with sd=0.001 is added to the responses Z and ZZ

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

Author(s)

Robert B. Gramacy, rbgramacy@chicagobooth.edu, and Matt Taddy, taddy@chicagobooth.edu

References

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). http://www.jstatsoft.org/v19/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. http://www.jstatsoft.org/v33/i06/.

Gramacy, R. B., Lee, H. K. H. (2007). Bayesian treed Gaussian process models with an application to computer modeling Journal of the American Statistical Association, to appear. Also available as ArXiv article 0710.4536 http://arxiv.org/abs/0710.4536

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

See Also

exp2d, exp2d.rand

Examples

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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")