Performs universal kriging
Performs universal kriging using X, the n \times k
design matrix for the regression coefficients of the observed
data, y, the n \times 1 matrix of observed responses,
V, the (positive definite) covariance matrix of the
observed responses, Xp, the np \times k design matrix
of the responses to be predicted, Vp, the
np \times np
covariance matrix of the responses to be predicted, and Vop,
the n \times np matrix of covariances between the observed
responses and the responses to be predicted. If user specifies nsim to be a positive integer, then nsim conditional realizations of the predictive distribution will be generated.
krige.uk(y, V, Vp, Vop, X, Xp, nsim = 0, Ve.diag = NULL, method = "eigen")
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 |
X |
The design matrix of the observed data. The size is n \times k |
Xp |
The design matrix of the responses to be predicted. The size is np \times k |
.
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. |
method |
The method for decomposing |
It is assumed that there are n observed data values
and that we wish to make predictions at np locations. We assume
that there are k regression coefficients (including the intercept).
Both X and Xp should contain a column of 1's if an intercept
is desired.
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.
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. |
coeff |
A vector of length k containing the estimated regression coefficients. |
vcov.coeff |
A k \times k matrix containing the (estimated) covariance matrix of estimated the regression coefficients. |
sim |
An n \times nsim matrix containing the |
If nsim > 0, this list has class "krigeConditionalSample".
Joshua French
Statistical Methods for Spatial Data Analysis, Schabenberger and Gotway (2003). See p. 241-243.
# create observed and predicted coordinates ocoords <- matrix(runif(100), ncol = 2) pcoords <- matrix(runif(200), ncol = 2) # include some observed locations in the predicted coordinates acoords <- rbind(ocoords, pcoords) # create design matrices X <- as.matrix(cbind(1, ocoords)) Xa <- as.matrix(cbind(1, acoords)) # create covariance matrix C3 <- cov.sp(coords = ocoords, sp.type = "matern", sp.par = c(2, 1), smoothness = 1, finescale = 0, error = 0.5, pcoords = acoords) # set values of regression coefficients coeff <- matrix(c(1, 2, 3), nrow = 1) # generate data with error y <- rmvnorm(nsim = 1, mu = tcrossprod(X, coeff), V = C3$V) + rnorm(50, sd = sqrt(.5)) # use universal kriging to make predictions. Do not do # conditional simulation krige.obj <- krige.uk(as.vector(y), V = C3$V, Vp = C3$Vp, Vop = C3$Vop, X = X, Xp = Xa, nsim = 0) #Do kriging with conditional simulation krige.obj2 <- krige.uk(as.vector(y), V = C3$V, Vp = C3$Vp, Vop = C3$Vop, X = X, Xp = Xa, nsim = 100, Ve.diag = rep(.5, 50), method = "eigen")
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