spMC: Continuous-Lag Spatial Markov Chains

Authors

Luca Sartore

Maintainer: Luca Sartore

Features of the package

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.

References

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].