Maintainer: Luca Sartore

The main goal of the **spMC** package is to provide a
set of functions for 1. the stratum lengths analysis along a chosen
direction, 2. fast estimation of continuous lag spatial Markov chains
model parameters and probability computing (also for large data sets),
3. transition probability maps and transiograms drawing, 4. simulation
methods for categorical random fields.

Several functions are available for the stratum lengths analysis, in particular they compute the stratum lengths for each stratum category, they compute the empirical distributions and many other tools for a graphical analysis.

Usually, the basic inputs for the most of the functions are a vector
of categorical data and their location coordinates. They are used to
estimate empirical transition probabilities (`transiogram`

),
to estimate model parameters (`tpfit`

for one-dimensional
Markov chains or `multi_tpfit`

for multidimensional Markov
chains). Once parameters are estimated, it’s possible to compute
theoretical transition probabilities by the use of the function
`predict.tpfit`

for one-dimensional Markov chains and
`predict.multi_tpfit`

for multidimensional ones.

The function `plot.transiogram`

allows to plot
one-dimensional transiograms, while `image.multi_tpfit`

permit to draw transition probability maps. A powerful tool to explore
graphically the anisotropy of such process is given by the functions
`pemt`

and `image.pemt`

, which let the user to
draw “quasi-empirical” transition probability maps.

Simulation methods are based on Indicator Kriging
(`sim_ik`

), Indicator Cokriging (`sim_ck`

), Fixed
or Random Path algorithms (`sim_path`

) and Multinomial
Categorical Simulation technique (`sim_mcs`

).

For a complete list of exported functions, use
`library(help = "spMC")`

once the **spMC**
package is installed.

Allard, D., D’Or, D., Froidevaux, R. (2011) An efficient maximum
entropy approach for categorical variable prediction. *European
Journal of Soil Science*, **62**(3), 381-393.

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

Dynkin, E. B. (1961) *Theory of Markov Processes*. Englewood
Cliffs, N.J.: Prentice-Hall, Inc.

Higham, N. J. (2008) *Functions of Matrices: Theory and
Computation*. Society for Industrial and Applied Mathematics.

Li, W. (2007) A Fixed-Path Markov Chain Algorithm for Conditional
Simulation of Discrete Spatial Variables. *Mathematical Geology*,
**39**(2), 159-176.

Li, W. (2007) Markov Chain Random Fields for Estimation of
Categorical Variables. *Mathematical Geology*,
**39**(June), 321-335.

Li, W. (2007) Transiograms for Characterizing Spatial Variability of
Soil Classes. *Soil Science Society of America Journal*,
**71**(3), 881-893.

Pickard, D. K. (1980) Unilateral Markov Fields. *Advances in
Applied Probability*, **12**(3), 655-671.

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

Sartore, L. (2013). spMC: Modelling Spatial Random Fields with
Continuous Lag Markov Chains. *The R Journal*,
**5**(2), 16-28.

Sartore, L., Fabbri, P. and Gaetan, C. (2016). spMC: an R-package for
3D lithological reconstructions based on spatial Markov chains.
*Computers & Geosciences*, **94**(September),
40-47.

Weise, T. (2009) *Global Optimization Algorithms - Theory and
Application*. http://www.it-weise.de/projects/book.pdf.