1d:T7b7,# Compute the log-marginal posterior of a kriging model, using the prior XXXY. ```r ## S3 method for class 'NuggetKriging' logMargPostFun(object, theta_alpha, return_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. - `return_grad`: Logical. Should the function return the gradient (w.r.t theta_alpha)? - `bench`: Logical. Should the function display benchmarking output - `...`: Not used. ## Returns The value of the log-marginal posterior computed for the given vector $\theta,\frac{\sigma^2}{\sigma^2+nugget}$. ## Examples ```r 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') ``` ## References XXXY A reference describing the model (prior, ...) ## See Also `rgasp` in the RobustGaSP package. ## Author(s) Yann Richet yann.richet@asnr.fr

logMargPostFun.NuggetKriging function