spMC (version 0.3.15)

predict.multi_tpfit: Compute Theoretical Multidimensional Transiograms

Description

The function computes theoretical transition probabilities of a \(d\)-D continuous-lag spatial Markov chain for a specified set of lags.

Usage

# S3 method for multi_tpfit
predict(object, lags, byrow = TRUE, ...)

Value

An object of the class multi_transiogram is returned. The print.multi_transiogram function is used to print computed probabilities. The object is a list with the following components:

Tmat

a 3-D array containing the probabilities.

lags

a matrix containing the lag vectors.

type

a character string which specifies that computed probabilities are theoretical.

Arguments

object

an object of the class multi_tpfit, typically with the output of the function multi_tpfit.

lags

a lag vector or matrix of \(d\)-D lags.

byrow

a logical value; if TRUE (by default), each row of matrix argument lags will be considered as a lag vector.

...

further arguments passed from other methods.

Author

Luca Sartore

Details

A \(d\)-D continuous-lag spatial Markov chain is probabilistic model which is developed by interpolation of the transition rate matrices computed for the main directions. It defines the transition probability \(\Pr(Z(s + h) = z_k | Z(s) = z_j)\) through the entry \(t_{jk}\) of the following matrix $$T = \mbox{expm} (\Vert h \Vert R),$$ where \(h\) is the lag vector and the entries of \(R\) are ellipsoidally interpolated.

References

Carle, S. F., Fogg, G. E. (1997) Modelling Spatial Variability with One and Multidimensional Continuous-Lag Markov Chains. Mathematical Geology, 29(7), 891-918.

Sartore, L. (2010) Geostatistical models for 3-D data. M.Phil. thesis, Ca' Foscari University of Venice.

See Also

multi_tpfit, print.multi_tpfit, image.multi_tpfit, tpfit, transiogram

Examples

# \donttest{
data(ACM)

# Estimate the parameters of a 
# multidimensional MC model
RTm <- multi_tpfit(ACM$MAT3, ACM[, 1:3])

# Generate the matrix of 
# multidimensional lags
lags <- expand.grid(X=-1:1, Y=-1:1, Z=-1:1)
lags <- as.matrix(lags)

# Compute transition probabilities 
# from the multidimensional MC model
predict(RTm, lags)
# }