`Kriging::logMargPost`

Description

Get the Maximized Log-Marginal Posterior Density of a Kriging Model

Usage

Python
```
# k = Kriging(...)
k.logMargPost()
```
R
```
# k = Kriging(...)
k$logMargPost()
```
Matlab/Octave
```
% k = Kriging(...)
k.logMargPost()
```

Details

Using the jointly robust prior $\pi_{\texttt{JR}}(\boldsymbol{\theta},\, \sigma^2, \, \boldsymbol{\beta})$ the marginal or integrated posterior is the function of $\boldsymbol{\theta}$ obtained from the posterior density by marginalizing out the GP variance $\sigma^2$ and the vector $\boldsymbol{\beta}$ of trend coefficients. See logMargPostFun.Kriging for the log-marginal posterior density. By maximizing this function w.r.t. $\boldsymbol{\theta}$ we get estimated correlation ranges which are warranted to be postitive and finite $0 < \theta_k < \infty$.

Value

The maximal value of the log-marginal posterior density, corresponding to the estimated value of the vector $\boldsymbol{\theta}$ of correlation ranges.

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="LMP")
print(k)

k$logMargPost()

Results

* data: 10x[0.0455565,0.940467] -> 10x[0.194057,1.00912]
* trend constant (est.): 0.388566
* variance (est.): 0.158896
* covariance:
  * kernel: matern3_2
  * range (est.): 0.313364
  * fit:
    * objective: LMP
    * optim: BFGS
[1] 10.64938

Kriging::logMargPost