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", "sim", "twovar"),
splitmin = 1, basemax = d, ...)The output is the following list of params...
dimension of regression coefficients \(
\beta\): 1 for input meanfn = "constant", or
ncol(X)+1 for meanfn = "linear"
copied from the inputs
copied from the inputs
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
rep(0,col) starting values for beta linear parameters
c(0.5,2,max(c(10,col+1)),1,d) indicating the tree prior
process parameters \(\alpha\), \(\beta\), minpart,
splitmin and basemax:
$$p_{\mbox{\tiny split}}(\eta, \mathcal{T}) =
\alpha*(1+\eta)^\beta$$
with zero probability given to trees
with partitions containing less than nmin data points;
splitmin indicates the first column of X which
where treed partitioning is allowed; basemax gives the
last column where the base model is used
c(5,10) \(\sigma^2\) inverse-gamma prior
parameters c(a0, g0) where g0 is rate parameter
c(5,10) \(\tau^2\) inverse-gamma
prior parameters c(a0, g0) where g0 is rate parameter
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 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.
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 rate parameters; default reduces to simple exponential prior;
specifying nug.p = 0 fixes the nugget parameter to the “starting”
value in gd[1], i.e., it is excluded from the MCMC
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 $$p(b|d)=t_1 +
\exp\left\{\frac{-g(t_2-t_1)}{d-0.5}\right\}$$
"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”
"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”
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”
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”
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 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.
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 rate parameters; default reduces to simple
exponential prior.
basemax * basemax RW-MVN
proposal covariance matrix for GP-SIM models; only appears when
corr="sim", the default is diag(rep(0.2, basemax))
number of input dimensions ncol(X)
A choice of mean function for the process. When
meanfn = "linear" (default), then we have the process
$$Z = (\mathbf{1} \;\; \mathbf{X}) \beta + W(\mathbf{X})$$
where \(W(\mathbf{X})\) represents the Gaussian process
part of the model (if present). Otherwise, when
meanfn = "constant", then$$Z = \beta_0 + W(\mathbf{X})$$
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") and single-index model
("sim") and "twovar" as “beta” functionality.
The option "mrexpsep" uses a multi-resolution GP model,
a depricated feature in the package
(docs removed)
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
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
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, 19(9). https://www.jstatsoft.org/v19/i09 tools:::Rd_expr_doi("10.18637/jss.v019.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. https://www.jstatsoft.org/v33/i06/ tools:::Rd_expr_doi("10.18637/jss.v033.i06")
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
Robert B. Gramacy, Heng Lian (2011). Gaussian process single-index models as emulators for computer experiments. Available as ArXiv article 1009.4241 https://arxiv.org/abs/1009.4241
blm, btlm, bgp,
btgp, bgpllm, btgpllm