Scalable approximations to kriging

VecchiaLoglik: Vecchia's approximate log-likelihood from the m nearest predecessors. NngpPredict: nearest-neighbour Gaussian process kriging. TaperedKriging: simple kriging with a Wendland tapered covariance. SparseGpKrige: subset of regressors, DTC (predictive process) and FITC (modified predictive process) through inducing points. FixedRankKriging: Cressie-Johannesson fixed rank kriging with bisquare bases and the Sherman-Morrison-Woodbury inverse. Covariance models as KrigingCovariance. Identical to the Python arm morie.fn.krigapprox.

Usage

VecchiaLoglik(z, coords, model, m = 10L, mean = 0)

NngpPredict(z, coords, new_coords, model, m = 10L, mean = NULL)

TaperedKriging(z, coords, new_coords, model, taper_range, mean = NULL)

SparseGpKrige(
  z,
  coords,
  new_coords,
  model,
  inducing,
  noise,
  method = "fitc",
  mean = NULL
)

FixedRankKriging(
  z,
  coords,
  new_coords,
  centers,
  radius,
  K,
  sigma2_eps,
  sigma2_xi = 0,
  mean = NULL
)

Arguments

z

Observations.

coords, new_coords

Matrices of data and target coordinates.

model

Covariance model.

m

Number of neighbours.

mean

Known constant mean (NULL: sample mean where allowed).

taper_range

Taper range.

inducing

Matrix of inducing points (knots).

noise

Noise (nugget) variance.

method

One of "sor", "dtc", "fitc".

centers

Matrix of basis-function centres.

radius

Basis radius (scalar or one per centre).

K

Covariance matrix of the basis coefficients.

sigma2_eps, sigma2_xi

Measurement-error and fine-scale variances.

Value

List.

References

Vecchia, A. V. (1988). Estimation and model identification for continuous spatial processes. Journal of the Royal Statistical Society B 50, 297-312.

Datta, A., Banerjee, S., Finley, A. O. and Gelfand, A. E. (2016). Hierarchical nearest-neighbor Gaussian process models for large geostatistical datasets. JASA 111, 800-812.

Furrer, R., Genton, M. G. and Nychka, D. (2006). Covariance tapering for interpolation of large spatial datasets. JCGS 15, 502-523.

Quinonero-Candela, J. and Rasmussen, C. E. (2005). A unifying view of sparse approximate Gaussian process regression. JMLR 6, 1939-1959.

Cressie, N. and Johannesson, G. (2008). Fixed rank kriging for very large spatial data sets. Journal of the Royal Statistical Society B 70, 209-226.

Examples

m <- list(model = "Exp", psill = 1, range = 1, nugget = 0.1)
VecchiaLoglik(c(0.2, -0.1, 0.4), rbind(c(0, 0), c(1, 0), c(0, 1)), m, 2)$loglik
#> [1] -2.870975