Kriging with change of support, nonstationarity and variogram uncertainty

AreaToPointKriging: Kyriakidis area-to-point (downscaling) kriging, coherent with the areal data. NonstationaryKriging: ordinary kriging with the Paciorek-Schervish nonstationary exponential covariance. EmpiricalVariogramBins: Matheron's binned sample variogram (gstat defaults). FitVariogramWls: nugget plus Exp, Gau or Sph variogram by weighted least squares (weights N/h^2). GaKriging: variogram fitted by a real-coded genetic algorithm, then ordinary kriging. EmpiricalBayesianKriging: kriging averaged over a likelihood-weighted spectrum of variograms refitted to simulations. Identical to the Python arm morie.fn.krigsupport.

Usage

AreaToPointKriging(values, supports, new_coords, model, mean = NULL)

NonstationaryKriging(z, coords, new_coords, ell, ell_new, sigma2, nugget = 0)

EmpiricalVariogramBins(z, coords, cutoff = NULL, width = NULL)

FitVariogramWls(ev, model = "Exp")

GaKriging(
  z,
  coords,
  new_coords,
  model = "Exp",
  pop = 40L,
  generations = 60L,
  seed = 1,
  ev = NULL
)

EmpiricalBayesianKriging(
  z,
  coords,
  new_coords,
  nsim = 50L,
  model = "Exp",
  seed = 1
)

Arguments

values: Areal data.
supports: List of matrices discretising each area.
new_coords: Matrix of target points.
model: Covariance model (KrigingCovariance), or model name (Exp, Gau, Sph) for the fitting functions.
mean: Known mean (simple kriging) or NULL.
z: Observations.
coords: Matrix of data coordinates.
ell, ell_new: Kernel scales at the data and at the targets.
sigma2: Partial sill.
nugget: Nugget variance.
cutoff, width: Variogram cutoff and bin width.
ev: Sample variogram (list with dist, gamma, np).
pop, generations: GA population size and generations.
seed: Philox seed.
nsim: Number of simulated variograms.

Value

List.

References

Kyriakidis, P. C. (2004). A geostatistical framework for area-to-point spatial interpolation. Geographical Analysis 36, 259-289.

Paciorek, C. J. and Schervish, M. J. (2006). Spatial modelling using a new class of nonstationary covariance functions. Environmetrics 17, 483-506.

Cressie, N. (1985). Fitting variogram models by weighted least squares. Mathematical Geology 17, 563-586.

Krivoruchko, K. (2012). Empirical Bayesian kriging. ArcUser, Fall 2012.

Examples

ev <- list(dist = c(0.5, 1, 1.5, 2), gamma = c(0.45, 0.72, 0.86, 0.93), np = c(10, 12, 14, 9))
FitVariogramWls(ev)$range
#> [1] 0.8973353