Lognormal kriging with the unbiased back-transform

Kriges \(Y = \log Z\); simple kriging back-transforms as \(\exp(\hat Y + \sigma^2/2)\), ordinary kriging as \(\exp(\hat Y + \sigma^2/2 - m)\) with \(m = -\mu\) the Lagrange multiplier of the variogram-form system (Journel 1980; Cressie 1993, eq. 3.2.40).

Usage

KrigeLognormal(z, coords, new_coords, model, beta = NULL)

Arguments

z

Observations.

coords

Matrix of locations (any dimension).

new_coords

Matrix of targets (block centres with block).

model

Covariance model (KrigingCovariance).

beta

Known mean of the log values (simple kriging).

Value

List with prediction, log_prediction, log_variance.

References

Journel, A. G. (1980). The lognormal approach to predicting local distributions of selective mining unit grades. Mathematical Geology 12, 285-303.

Examples

m <- list(model = "Exp", psill = 0.3, range = 2)
KrigeLognormal(c(1, 3, 2), rbind(c(0, 0), c(2, 0), c(0, 2)), rbind(c(1, 1)), m)$prediction
#> [1] 2.027853