Description Usage Arguments Details Value Note Author(s) References See Also

Generate X and Y values from the 10-dim “first” Friedman data set used to validate the Multivariate Adaptive Regression Splines (MARS) model, and a variation involving boolean indicators. This test function has three non-linear and interacting variables, along with two linear, and five which are irrelevant. The version with indicators has parts of the response turned on based on the setting of the indicators

1 2 | ```
friedman.1.data(n = 100)
fried.bool(n = 100)
``` |

`n` |
Number of samples desired |

In the original formulation, as implemented by `friedman.1.data`

the function has 10-dim inputs `X`

are drawn from Unif(0,1), and responses
are *N(m(X),1)* where
*m(X) = E[f(X)]* and

*m(X) = 10*sin(pi*X[,1]*X[,2]) + 20*(X[,3]-0.5)^2 + 10*X[,4] + 5*X[,5]*

The variation `fried.bool`

uses indicators
*I in 1:4*. The function also has 10-dim
inputs `X`

with columns distributed as Unif(0,1) and responses
are *N(m(X,I), 1)* where
*m(X,I) = E[f(X,I)]* and

*m(X,I) = fI(X) if I in 1:3 else m(X[,10:1])*

where

*f1(X)=10*sin(pi*X[,1]*X[,2]), f2(X)=20*(X[,3]-0.5)^2, f3(X)=10*X[,4]+5*X[,5] *

The indicator I is coded in binary in the output data frame as:
`c(0,0,0)`

for `I=1`

,
`c(0,0,1)`

for `I=2`

,
`c(0,1,0)`

for `I=3`

, and
`c(1,0,0)`

for `I=4`

.

Output is a `data.frame`

with columns

`X.1, ..., X.10 ` |
describing the 10-d randomly sampled inputs |

`I.1, ..., I.3` |
boolean version of the indicators provided only
for |

`Y` |
sample responses (with N(0,1) noise) |

`Ytrue` |
true responses (without noise) |

An example using the original version of the data
(`friedman.1.data`

) is contained in the first package vignette:
`vignette("tgp")`

. The boolean version `fried.bool`

is used in second vignette `vignette("tgp2")`

Robert B. Gramacy, rbg@vt.edu, and Matt Taddy, mataddy@amazon.com

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,

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,

Friedman, J. H. (1991).
*Multivariate adaptive regression splines.*
“Annals of Statistics”, **19**, No. 1, 1–67.

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

Chipman, H., George, E., \& McCulloch, R. (2002).
*Bayesian treed models.*
Machine Learning, **48**, 303–324.

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

`bgpllm`

, `btlm`

,
`blm`

, `bgp`

, `btgpllm`

, `bgp`

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