tgp.default.params {tgp} | R Documentation |
Construct a default list of parameters to the b*
functions– the interfaces to treed Gaussian process
modeling
tgp.default.params(d, meanfn = c("linear", "constant"), corr = c("expsep", "exp", "mrexpsep", "matern"), splitmin = 1, basemax = d, ...)
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
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 |
splitmin |
Indicates which column of the inputs X should
be the first to allow splits via treed partitioning. This is useful
for excluding certain input directions from the partitioning
mechanism |
basemax |
Indicates which column of the inputs X should
be the last be fit under the base model (e.g., LM or GP). This is useful
for allowing some input directions (e.g., binary indicators) to only
influence the tree partitioning mechanism, and not the base model(s)
at the leaves of the tree |
... |
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 |
The output is the following list of params
...
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" ,
"bmzt" , or "bmznot" 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(0.5,2,max(c(10,col+1)),1) indicating the tree prior
process parameters alpha, beta, minpart
and splitmin:
p(split leaf eta) = alpha*(1+depth(eta))^(-beta)
with zero probability given to trees
with partitions containing less than |
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;
specifying nug.p = 0 fixes the nugget parameter to the “starting”
value in gd[0] , i.e., it is excluded from the MCMC |
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.
|
Please refer to the examples for the functions in
"See Also" below, vignette("tgp")
and vignette(tgp2)
Robert B. Gramacy, rbgramacy@ams.ucsc.edu, and Matt Taddy, taddy@ams.ucsc.edu
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. (2007). Bayesian treed Gaussian process models with an application to computer modeling Journal of the American Statistical Association, to appear. Also available as as ArXiv article 0710.4536 http://arxiv.org/abs/0710.4536
http://www.ams.ucsc.edu/~rbgramacy/tgp.html
blm
, btlm
, bgp
,
btgp
, bgpllm
, btgpllm