spMC (version 0.3.15)

predict.tpfit: Compute Theoretical One-dimensional Transiograms

Description

The function computes theoretical transition probabilities of a 1-D continuous-lag spatial Markov chain for a specified set of lags.

Usage

# S3 method for tpfit
predict(object, lags, ...)

Value

An object of the class transiogram is returned. The function print.transiogram 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 vector containing one-dimensional lags.

type

a character string which specifies that computed probabilities are theoretical.

Arguments

object

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

lags

a vector of 1-D lags.

...

further arguments passed from other methods.

Author

Luca Sartore

Details

A 1-D continuous-lag spatial Markov chain is probabilistic model which involves a transition rate matrix \(R\) computed for the direction \(\phi\). It defines the transition probability \(\Pr(Z(s + h) = z_k | Z(s) = z_j)\) through the entry \(t_{jk}\) of the following matrix $$T = \mbox{expm} (h R),$$ where \(h\) is a positive lag value.

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

tpfit, print.tpfit, plot.transiogram, transiogram, multi_tpfit

Examples

# \donttest{
data(ACM)

# Estimate the parameters of a 
# one-dimensional MC model
RTm <- tpfit(ACM$MAT3, ACM[, 1:3], c(0, 0, 1))

# Compute transition probabilities 
# from the one-dimensional MC model
predict(RTm, lags = 0:2/2)
# }