`NuggetKriging::logLikelihood`

Description

Get the Maximized Log-Likelihood of a NuggetKriging Model Object

Usage

Python

# k = NuggetKriging(...)
k.logLikelihood()

R
```
k$logLikelihood()
```

Matlab/Octave

% k = NuggetKriging(...)
k.logLikelihood()

Details

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

Value

The value of the maximized profile log-likelihood $\ell_{\texttt{prof}}(\widehat{\boldsymbol{\theta}},\,\widehat{\alpha})$ where $\alpha:= \sigma^2 / (\sigma^2 + \nu^2)$ is the ratio of the variances $\sigma^2$ for the GP and $\sigma^2 + \nu^2$ for the GP $+$ nugget. This is also the value $\ell(\widehat{\boldsymbol{\theta}},\, \widehat{\alpha},\, \widehat{\sigma}^2,\, \widehat{\boldsymbol{\beta}})$ or $\ell(\widehat{\boldsymbol{\theta}},\, \widehat{\sigma}^2,\, \widehat{\tau}^2, \, \widehat{\boldsymbol{\beta}})$ 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) + 0.1 * rnorm(nrow(X))

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

k$logLikelihood()

Results

* 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
[1] 4.95114

Reference

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

NuggetKriging::logLikelihood