# The Treed Gaussian Process Model Package

### Description

A Bayesian nonstationary nonparametric regression and design package implementing an array of models of varying flexibility and complexity.

### Details

This package implements Bayesian nonstationary, semiparametric nonlinear regression with “treed Gaussian process models” with jumps to the limiting linear model (LLM). The package contains functions which facilitate inference for seven regression models of varying complexity using Markov chain Monte Carlo (MCMC): linear model, CART (Classification and Regression Tree), treed linear model, Gaussian process (GP), GP with jumps to the LLM, GP single-index models, treed GPs, treed GP LLMs, and treed GP single-index models. R provides an interface to the C/C++ backbone, and a serves as mechanism for graphically visualizing the results of inference and posterior predictive surfaces under the models. A Bayesian Monte Carlo based sensitivity analysis is implemented, and multi-resolution models are also supported. Sequential experimental design and adaptive sampling functions are also provided, including ALM, ALC, and expected improvement. The latter supports derivative-free optimization of noisy black-box functions.

For a fuller overview including a complete list of functions, demos and
vignettes, please use `help(package="tgp")`

.

### 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

Robert B. Gramacy, Heng Lian (2011).
*Gaussian process single-index models as emulators for computer
experiments*. Available as ArXiv article 1009.4241
http://arxiv.org/abs/1009.4241

Gramacy, R. B., Lee, H. K. H. (2006).
*Adaptive design of supercomputer experiments.*
Available as UCSC Technical Report ams2006-02.

Gramacy, R.B., Samworth, R.J., and King, R. (2007)
*Importance Tempering.* ArXiV article 0707.4242
http://arxiv.org/abs/0707.4242

Gray, G.A., Martinez-Canales, M., Taddy, M.A., Lee, H.K.H., and
Gramacy, R.B. (2007) *Enhancing Parallel Pattern Search Optimization with
a Gaussian Process Oracle*, SAND2006-7946C, Proceedings of the NECDC