krige.sk {SpatialTools}

Performs simple kriging

Description

Performs simple kriging using y, a vector of length n, V, the (positive definite) covariance matrix of the observed responses, Vp, the np \times np covariance matrix of the responses to be predicted, Vop, the n \times np matrix of covariances between the observed responses and the responses to be predicted, and m, a numeric vector of length 1 identifying the value of the mean for each response.

Usage

	krige.sk(y, V, Vp, Vop, m = 0, nsim = 0, Ve.diag = NULL, method = "eigen")

Arguments

y

The vector of observed responses. Should be a matrix of size n \times 1 or a vector of length n.

V

The covariance matrix of the observed responses. The size is n \times n.

Vp

The covariance matrix of the responses to be predicted. The size is np \times np

Vop

The cross-covariance between the observed responses and the responses to be predicted. The size is n \times np.

m

A numeric vector of length 1 giving the mean of each response.

nsim

The number of simulated data sets to sample from the conditional predictive distribution.

Ve.diag

A vector of length n specifying the measure error variances of the observed data. Only needed if nsim > 0.

method

The method for decomposing V in conditional simulation. Default is "eigen", for the Eigen decomposition. Alternatives are "chol" (Cholesky) and "svd" (Singular Value Decomposition).

Details

It is assumed that there are n observed data values and that we wish to make predictions at np locations. The mean is subtracted from each value of y before determining the kriging weights, and then the mean is added onto the predicted response.

If doing conditional simulation, the Cholesky decomposition should not work when there are coincident locations between the observed data locations and the predicted data locations. Both the Eigen and Singular Value Decompositions should work.

If user specifies nsim to be a positive integer, then nsim conditional realizations of the predictive distribution will be generated. If this is less than 1, then no conditional simulation is done. If nsim is a positive integer, then Ve.diag must also be supplied. Ve.diag is should be a vector of length n specifying the measurement error variances of the observed data. This information is only used for conditional simulation, so this argument is only needed when nsim > 0. When conditional simulation is desired, then the argument method can be to specify the method used to decompose V. Options are "eigen", "chol", or "svd" (Eigen decomposition, Cholesky decomposition, or Singular value decomposition, respectively). This information is only used for conditional simulation, so this argument is only applicable when nsim > 0.

Value

The function returns a list containing the following objects:

pred

A vector of length np containing the predicted responses.

mspe

A vector of length np containing the mean-square prediction error of the predicted responses.

simulations

An n \times nsim matrix containing the nsim realizations of the conditional realizations. Each column of the matrix represents a realization of the conditional normal distribution.

mean

The mean value (m) originally provided to the function

. If nsim > 0, this list has class "krigeConditionalSample".

Author(s)

Joshua French

References

Statistical Methods for Spatial Data Analysis, Schabenberger and Gotway (2003). See p. 226-228.

Examples

	data(toydata)
	y <- as.vector(toydata$y)
	V <- toydata$V
	Vp <- toydata$Vp
	Vop <- toydata$Vop
	krige.sk(y, V, Vp, Vop, m = 2)