logMargPostFun.NuggetKriging {rlibkriging}

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 class 'NuggetKriging'
logMargPostFun(object, theta_alpha, grad = FALSE, bench = FALSE, ...)

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.

grad

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

bench

Logical. Should the function display benchmarking output

...

Not used.

Value

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

Author(s)

Yann Richet [e-mail]

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')