rlibkriging (version 0.9-1)

logMargPostFun.NuggetKriging: Compute the log-marginal posterior of a kriging model, using the prior XXXY.

Description

Compute the log-marginal posterior of a kriging model, using the prior XXXY.

Usage

# S3 method for NuggetKriging
logMargPostFun(object, theta_alpha, return_grad = FALSE, bench = FALSE, ...)

Value

The value of the log-marginal posterior computed for the given vector \(\boldsymbol{theta_alpha}\).

Arguments

object

S3 NuggetKriging object.

theta_alpha

Numeric vector of correlation range and variance over variance plus nugget parameters at which the function is to be evaluated.

return_grad

Logical. Should the function return the gradient (w.r.t theta_alpha)?

bench

Logical. Should the function display benchmarking output

...

Not used.

Author

Yann Richet

References

XXXY A reference describing the model (prior, ...)

See Also

rgasp in the RobustGaSP package.

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, "matern3_2", objective="LMP")
print(k)

theta0 = k$theta()
lmp_alpha <- function(alpha) k$logMargPostFun(cbind(theta0,alpha))$logMargPost
a <- seq(from = 0.9, to = 1.0, length.out = 101)
plot(a, Vectorize(lmp_alpha)(a), type = "l",xlim=c(0.9,1))
abline(v = k$sigma2()/(k$sigma2()+k$nugget()), col = "blue")

alpha0 = k$sigma2()/(k$sigma2()+k$nugget())
lmp_theta <- function(theta) k$logMargPostFun(cbind(theta,alpha0))$logMargPost
t <- seq(from = 0.001, to = 2, length.out = 101)
plot(t, Vectorize(lmp_theta)(t), type = 'l')
abline(v = k$theta(), col = "blue")

lmp <- function(theta_alpha) k$logMargPostFun(theta_alpha)$logMargPost
t <- seq(from = 0.4, to = 0.6, length.out = 51)
a <- seq(from = 0.9, to = 1, length.out = 51)
contour(t,a,matrix(ncol=length(t),lmp(expand.grid(t,a))),
 nlevels=50,xlab="theta",ylab="sigma2/(sigma2+nugget)")
points(k$theta(),k$sigma2()/(k$sigma2()+k$nugget()),col='blue')