Kriging::logLikelihood

Description

Get the Maximized Log-Likelihood of a Kriging Model Object

Usage

  • Python

    # k = Kriging(...)
k.logLikelihood()

  • R

    # k = Kriging(...)
k$logLikelihood()

  • Matlab/Octave

    % k = Kriging(...)
k.logLikelihood()

Details

See logLikelihoodFun.Kriging for more details on the profile log-likelihood function used in the maximization.

Value

The value of the maximized profile log-likelihood \(\ell_{\texttt{prof}}(\widehat{\boldsymbol{\theta}})\). This is also the value \(\ell(\widehat{\boldsymbol{\theta}},\, \widehat{\sigma}^2,\, \widehat{\boldsymbol{\beta}})\) of the maximized log-likelihood.

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)

k <- Kriging(y, X, kernel = "matern3_2", objective="LL")
print(k)

k$logLikelihood()

Results

* data: 10x[0.0455565,0.940467] -> 10x[0.194057,1.00912]
* trend constant (est.): 0.433954
* variance (est.): 0.0873685
* covariance:
  * kernel: matern3_2
  * range (est.): 0.240585
  * fit:
    * objective: LL
    * optim: BFGS
[1] 8.62771

Reference