NoiseKriging::logLikelihood

Description

Get the Maximized Log-Likelihood of a NoiseKriging Model Object

Usage

  • Python

    # k = NoiseKriging(...)
    k.logLikelihood()
    
  • R

    # k = NoiseKriging(...)
    k$logLikelihood()
    
  • Matlab/Octave

    % k = NoiseKriging(...)
    k.logLikelihood()
    

Details

See logLikelihoodFun.NoiseKriging for more details on the corresponding profile log-likelihood function.

Value

The value of the maximized profile log-likelihood \(\ell_{\texttt{prof}}(\widehat{\boldsymbol{\theta}},\,\widehat{\sigma}^2)\). This is also the maximized value \(\ell(\widehat{\boldsymbol{\theta}},\, \widehat{\sigma}^2,\, \widehat{\boldsymbol{\beta}})\) of the 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) + X/10 * rnorm(nrow(X))

k <- NoiseKriging(y, (X/10)^2, X, kernel = "matern3_2", objective="LL")
print(k)

k$logLikelihood()

Results

* data: 10x[0.0455565,0.940467] -> 10x[0.152144,0.957381]
* trend constant (est.): 0.487335
* variance (est.): 0.0635381
* covariance:
  * kernel: matern3_2
  * range (est.): 0.211413
  * noise: 0.000827008, 0.00621425, 0.00167262, 0.0077972, 0.00884479, 2.07539e-05, 0.00278895, 0.00796412, 0.00304081, 0.00208497
  * fit:
    * objective: LL
    * optim: BFGS
[1] 5.200129

Reference