`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]
  * noise: 10x[2.07539e-05,0.00884479]
* trend constant (est.): 0.487335
* variance (est.): 0.0635381
* covariance:
  * kernel: matern3_2
  * range (est.): 0.211413
  * fit:
    * objective: LL
    * optim: BFGS
[1] 5.200129

Reference

Code: https://github.com/libKriging/libKriging/blob/master/src/lib/NoiseKriging.cpp#L94

NoiseKriging::logLikelihood