spMC (version 0.2.2)

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 class '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:Tmata 3-D array containing the probabilities.lagsa matrix containing the lag vectors.typea character string which specifies that computed probabilities are theoretical.

Rdversion

1.1

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

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)