spMC (version 0.2.2)

transiogram: Empirical Transition Probabilities Estimation for 1-D MC

Description

The function estimates transition probabilities matrices for a $1$-D continuous lag spatial Markov chain.

Usage

transiogram(data, coords, direction, max.dist = Inf, 
            mpoints = 20, tolerance = pi / 8)

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:Tmata 3-D array containing the probabilities.lagsa vector containing one-dimensional lags.typea character string which specifies that computed probabilities are empirical.

Rdversion

1.1

Details

Empirical probabilities are estimated by counting such pairs of observations which satisfy some properties, and by normalizing the result.

A generic pair of sample points $s_i$ and $s_j$, where $i \neq j$, must satisfy the following properties:

• $\Vert s_i - s_j \Vert \in [a, a+\frac{m}{n}],$where$a$is a non negative real value, while$m$denotes the maximum lag value (max.dist) and$n$is the number of lag intervals (mpoints).
• the lag vector$h = s_i - s_j$must have the same direction of the vector$\phi$(direction) with a certain angulartolerance.

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

predict.tpfit, predict.tpfit, plot.transiogram

Examples

data(ACM)

# Estimate empirical transition 
# probabilities by points
transiogram(ACM$MAT3, ACM[, 1:3], c(0, 0, 1), 200, 5)