tgp.default.params {tgp}R Documentation

Default Treed Gaussian Process Model Parameters

Description

Construct a default list of parameters to the b* functions– the interfaces to treed Gaussian process modeling

Usage

tgp.default.params(d, meanfn = c("linear", "constant"),
                   corr = "expsep", ...)

Arguments

d number of input dimensions ncol(X)
meanfn A choice of mean function for the process. When meanfn = "linear" (default), then we have the process

Z = cbind(rep(1,nrow(X), X)) %*% beta + W(X),

where W(X) represents the Gaussian process part of the model (if present). Otherwise, when meanfn = "constant", then

Z = beta0 + W(X).

corr Gaussian process correlation model. Choose between the isotropic power exponential family ("exp") or the separable power exponential family ("expsep", default); the current version also supports the isotropic Matern ("matern") as “beta” functionality. The option "mrexpsep" uses a multi-resolution GP model.
... These ellipses arguments are interpreted as augmentations to the prior specification. You may use these to specify a custom setting of any of default parameters in the output list detailed below

Value

The output is the following list of params...

tree c(0.5,2,max(c(10,col+1)),1) indicating the tree prior parameters alpha, beta, minpart and splitmin
col dimension of regression coefficients beta: 1 for input meanfn = "constant", or ncol(X)+1 for meanfn = "linear"
meanfn copied from the inputs
corr copied from the inputs
bprior Linear (beta) prior, default is "bflat" which gives an “improper” prior which can perform badly when the signal-to-noise ratio is low. In these cases the “proper” hierarchical specification "b0" or "bmzt" prior may perform better
start c(0.5,0.1,1.0,1.0) starting values for range d, nugget g, s2, and tau2
beta rep(0,col) starting values for beta linear parameters
tree c(0.25,2,min(c(10,col+1))) tree prior process parameters c(alpha, beta, nmin) specifying

p(split leaf eta) = alpha*(1+depth(eta))^(-beta)

with zero probability given to trees with partitions containing less than nmin data points

s2.p c(5,10) s2 inverse-gamma prior parameters c(a0, g0) where g0 is scale (1/rate) parameter
tau2.p c(5,10) tau2 inverse-gamma prior parameters c(a0, g0) where g0 is scale (1/rate) parameter
d.p c(1.0,20.0,10.0,10.0) Mixture of gamma prior parameter (initial values) for the range parameter(s) c(a1,g1,a2,g2) where g1 and g2 are scale (1/rate) parameters. If corr="mrexpsep", then this is a vector of length 8: The first four parameters remain the same and correspond to the "coarse" process, and the second set of four values, which default to c(1,10,1,10), are the equivalent prior parameters for the range parameter(s) in the residual "fine" process.
nug.p c(1,1,1,1) Mixture of gamma prior parameter (initial values) for the nugget parameter c(a1,g1,a2,g2) where g1 and g2 are scale (1/rate) parameters; default reduces to simple exponential prior
gamma c(10,0.2,10) LLM parameters c(g, t1, t2), with growth parameter g > 0 minimum parameter t1 >= 0 and maximum parameter t1 >= 0, where t1 + t2 <= 1 specifies

p(b|d)= t1 + exp(-g*(t2-t1)/(d-0.5))

d.lam "fixed" Hierarchical exponential distribution parameters to a1, g1, a2, and g2 of the prior distribution for the range parameter d.p; "fixed" indicates that the hierarchical prior is “turned off”
nug.lam "fixed" Hierarchical exponential distribution parameters to a1, g1, a2, and g2 of the prior distribution for the nug parameter nug.p; "fixed" indicates that the hierarchical prior is “turned off”
s2.lam c(0.2,10) Hierarchical exponential distribution prior for a0 and g0 of the prior distribution for the s2 parameter s2.p; "fixed" indicates that the hierarchical prior is “turned off”
tau2.lam c(0.2,0.1) Hierarchical exponential distribution prior for a0 and g0 of the prior distribution for the s2 parameter tau2.p; "fixed" indicates that the hierarchical prior is “turned off”
delta.p c(1,1,1,1) Parameters in the mixture of gammas prior on the delta scaling parameter for corr="mrexpsep": c(a1,g1,a2,g2) where g1 and g2 are scale (1/rate) parameters; default reduces to simple exponential prior. Delta scales the variance of the residual "fine" process with respect to the variance of the underlying "coarse" process.
nugf.p c(1,1,1,1) Parameters in the mixture of gammas prior on the residual "fine" process nugget parameter for corr="mrexpsep": c(a1,g1,a2,g2) where g1 and g2 are scale (1/rate) parameters; default reduces to simple exponential prior.

Note

Please refer to the examples for the functions in "See Also" below and vignette("tgp")

Author(s)

Robert B. Gramacy, rbgramacy@ams.ucsc.edu
Matt Taddy, taddy@ams.ucsc.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 Gramacy, R. B., Lee, H. K. H. (2006). Bayesian treed Gaussian process models. Available as UCSC Technical Report ams2006-01.

http://www.ams.ucsc.edu/~rbgramacy/tgp.html

See Also

blm, btlm, bgp, btgp, bgpllm, btgpllm


[Package tgp version 2.0-1 Index]