NuggetKriging::fit

Description

Fit a NuggetKriging Model Object using given Observations

Usage

• Python

  # k = NuggetKriging(kernel=...)
  k.fit(y, X, 
        regmodel = "constant",
        normalize = False,
        optim = "BFGS",
        objective = "LL",
        parameters = None)
  

• R

  # k = NuggetKriging(kernel=...)
  k$fit(y, X, 
        regmodel = "constant",
        normalize = FALSE,
        optim = "BFGS",
        objective = "LL",
        parameters = NULL)
  

• Matlab/Octave

  % k = NuggetKriging(kernel=...)
  k.fit(y, X, 
        regmodel = "constant",
        normalize = false,
        optim = "BFGS",
        objective = "LL",
        parameters = [])
  

Arguments

Argument	Description
y	Numeric vector of response values.
X	Numeric matrix of input design.
regmodel	Universal NuggetKriging linear trend: "constant", "linear", "interactive", "quadratic".
normalize	Logical. If TRUE both the input matrix X and the response y in normalized to take values in the interval \([0, 1]\) .
optim	Character giving the Optimization method used to fit hyper-parameters. Possible values are: "BFGS" and "none" , the later simply keeping the values given in parameters . The method "BFGS" uses the gradient of the objective (note that "BGFS10" means 10 multi-start of BFGS).
objective	Character giving the objective function to optimize. Possible values are: "LL" for the Log-Likelihood and "LMP" for the Log-Marginal Posterior.
parameters	Initial values for the hyper-parameters. When provided this must be named list with some elements "sigma2" , "theta" , "nugget" containing the initial value(s) for the variance, range and nugget parameters. If theta is a matrix with more than one row, each row is used as a starting point for optimization.
kernel	Character defining the covariance model: "exp" , "gauss" , "matern3_2" , "matern5_2" .

Details

The hyper-parameters (variance and vector of correlation ranges) are estimated thanks to the optimization of a criterion given by objective , using the method given in optim .

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))

k <- NuggetKriging("matern3_2")
print("before fit")
print(k)

k$fit(y,X)
print("after fit")
print(k)

Results

[1] "before fit"
* covariance:
  * kernel: matern3_2
[1] "after fit"
* data: 10x[0.0455565,0.940467] -> 10x[0.149491,0.940566]
* trend constant (est.): 0.488156
* variance (est.): 0.078856
* covariance:
  * kernel: matern3_2
  * range (est.): 0.274956
  * nugget (est.): 0.00347513
  * fit:
    * objective: LL
    * optim: BFGS