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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].

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Version

Install

install.packages('spMC')

Monthly Downloads

357

Version

0.3.15

License

GPL (>= 2)

Maintainer

Last Published

May 3rd, 2023

Functions in spMC (0.3.15)

getlen

Estimation of Stratum Lengths for Embedded Markov Chain
is.tpfit

Object test for tpfit class
mlen

Mean Length Estimation for Embedded Markov Chain
multi_tpfit_me

Maximum Entropy Method for Multidimensional Model Parameters Estimation
is.pemt

Images with Multi-direct`ional Transiograms
multi_tpfit_ils

Iterated Least Squares Method for Multidimensional Model Parameters Estimation
is.multi_tpfit

Object test for multi_tpfit class
multi_tpfit

Multidimensional Model Parameters Estimation
mixplot

Plot of Multiple One-dimensional Transiograms
is.transiogram

Object test for transiogram class
persp.multi_tpfit

Perspective Plots with Multidimensional Transiograms
is.multi_transiogram

Object test for multi_transiogram class
plot.lengths

Plot Stratum Lengths
pemt

Multi-directional Transiograms Estimation
setCores

Set the number of CPU cores for HPC
print.multi_tpfit

Printing Model Parameters for Multidimensional Continuous Lag Spatial MC
print.transiogram

Printing Theoretical or Empirical One-dimensional Transiograms
plot.density.lengths

Plot Empirical Densities Estimates of Stratum Lengths
plot.hist.lengths

Plot Histograms of Stratum Lengths
plot.transiogram

Plot One-dimensional Transiograms
predict.multi_tpfit

Compute Theoretical Multidimensional Transiograms
print.summary.lengths

Printing Stratum Lengths Summary for Each Observed Category
persp.pemt

Perspective Plots with Multi-directional Transiograms
predict.tpfit

Compute Theoretical One-dimensional Transiograms
multi_tpfit_ml

Mean Length Method for Multidimensional Model Parameters Estimation
print.tpfit

Printing Model Parameters for One-dimensional Continuous Lag Spatial MC
sim

Random Field Simulation
sim_ck

Conditional Simulation Based on Indicator Cokriging
tpfit_me

Maximum Entropy Method for One-dimensional Model Parameters Estimation
tpfit_ml

Mean Length Method for One-dimensional Model Parameters Estimation
quench

Conditional Simulation Adjuster Via Quenching Algorithm
sim_ik

Conditional Simulation Based on Indicator Kriging
print.density.lengths

Printing Empirical Densities Estimates of Stratum Lengths
spMC-package

Continuous Lag Spatial Markov Chains
print.multi_transiogram

Printing Theoretical Multidimensional Transiograms
tpfit

One-dimensional Model Parameters Estimation
print.lengths

Printing Stratum Lengths for Each Observed Category
tpfit_ils

Iterated Least Squares Method for One-dimensional Model Parameters Estimation
sim_mcs

Multinomial Categorical Simulation
sim_path

Conditional Simulation Based on Path Algorithms
summary.lengths

Summarizing Stratum Lengths
transiogram

Empirical Transition Probabilities Estimation for 1-D MC
which_lines

Points Classification through Directional Lines
boxplot.lengths

Stratum Lengths Boxplot
hist.lengths

Histograms of Stratum Lengths for Each Observed Category
ACM

ACM Data
embed_MC

Transition Probabilities Estimation for Embedded Markov Chain
density.lengths

Empirical Densities Estimation of Stratum Lengths
is.lengths

Object test for lengths class
contour.pemt

Display Contours with Multi-directional Transiograms
image.pemt

Images with Multi-directional Transiograms
image.multi_tpfit

Images with Multidimensional Transiograms