gp.optim {GPBayes}

A wraper to fit a Gaussian stochastic process model with optimization methods

Description

This function is a wraper to estimate parameters in the GaSP model with different choices of estimation methods using numerical optimization methods.

Usage

gp.optim(obj, method = "MMLE", opt = NULL, bound = NULL)

Arguments

obj

an S4 object gp

method

a string indicating the parameter estimation method:

MPLE

This indicates that the maximum profile likelihood estimation (MPLE) is used.

MMLE

This indicates that the maximum marginal likelihood estimation (MMLE) is used.

MAP

This indicates that the marginal/integrated posterior is maximized.

opt

a list of arguments to setup the optim routine. Current implementation uses three arguments:

method

The optimization method: Nelder-Mead or L-BFGS-B.

lower

The lower bound for parameters.

upper

The upper bound for parameters.

bound

Default value is NULL. Otherwise, it should be a list containing the following elements depending on the covariance class:

nugget

a list of bounds for the nugget parameter. It is a list containing lower bound lb and upper bound ub with default value list(lb=0, ub=Inf).

range

a list of bounds for the range parameter. Tt has default value range=list(lb=0, ub=Inf) for the Confluent Hypergeometric covariance, the Matérn covariance, exponential covariance, Gaussian covariance, powered-exponential covariance, and Cauchy covariance. The log of range parameterization is used: \log(\phi).

tail

a list of bounds for the tail decay parameter. It has default value list(lb=0, ub=Inf)

for the Confluent Hypergeometric covariance and the Cauchy covariance.

nu

a list of bounds for the smoothness parameter. It has default value list(lb=0, ub=Inf) for the Confluent Hypergeometric covariance and the Matérn covariance. when the powered-exponential or Cauchy class is used, it has default value nu=list(lb=0, ub=2). This can be achived by specifying the lower bound in opt.

Value

a list of updated gp object obj and fitted information fit

Author(s)

Pulong Ma [e-mail]

See Also

GPBayes-package, GaSP, gp, gp.mcmc

Examples

 
code = function(x){
y = (sin(pi*x/5) + 0.2*cos(4*pi*x/5))*(x<=9.6) + (x/10-1)*(x>9.6) 
return(y)
}
n=100
input = seq(0, 20, length=n)
XX = seq(0, 20, length=99)
Ztrue = code(input)
set.seed(1234)
output = Ztrue + rnorm(length(Ztrue), sd=0.1)
obj = gp(formula=~1, output, input, 
        param=list(range=4, nugget=0.1,nu=2.5),
        smooth.est=FALSE,
        cov.model=list(family="matern", form="isotropic"))
        
fit.optim = gp.optim(obj, method="MPLE")