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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. [Archived copy].
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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