# 2-d Exponential Data

### Description

A 2-dimensional data set that can be used to validate non-stationary models.

### Usage

1 |

### Format

A `data frame`

with 441 observations on the following 4 variables.

`X1`

Numeric vector describing the first dimension of

`X`

inputs`X2`

Numeric vector describing the second dimension of

`X`

inputs`Z`

Numeric vector describing the response

`Z(X)+N(0,sd=0.001)`

`Ztrue`

Numeric vector describing the true response

`Z(X)`

, without noise

### Details

The true response is evaluated as

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

Zero-mean normal noise
with `sd=0.001`

has been added to the true response

### Note

This data is used in the examples of the functions listed below in
the “See Also” section via the `exp2d.rand`

function

### 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.rand`

, `exp2d.Z`

,
`btgp`

, and other `b*`

functions