Parameter estimation of seeding and contamination rates in a subcritical percolation model with colouring on a triangular lattice, using the method of simulated moments (MSM). Code implementation in MATLAB (The MathWorks, Inc.).
Felix Beck, Bence Mélykúti (University of Freiburg, Germany).
2015-2017
With questions or comments, please contact Bence Mélykúti.
Felix Beck, Bence Mélykúti.
Parameter estimation in a subcritical percolation model with colouring,
Stochastics: An International Journal of Probability and Stochastic Processes, 91(5), 657–694, 2019, doi:10.1080/17442508.2018.1539089 (open access),
or arXiv:1604.08908
An additional MATLAB file must be downloaded!
fminsearchbnd:
- fminsearchbnd.m behaves similarly to fminsearch, except you can add bound constraints.
- source and description: http://de.mathworks.com/matlabcentral/fileexchange/8277-fminsearchbnd--fminsearchcon/content/FMINSEARCHBND/fminsearchbnd.m
- author: John D'Errico
- msm.m is the main file to be run for parameter estimation. It contains comments about variables and input requirements.
- createsynthdata.m is a tool to generate and save random realisations of the percolation process with colouring.
- plot_figure.m is a versatile plotting program to display lattices with our percolation process from saved data.
- latex_table.m, latex_table5.m and latex_table6.m created Tables 1-4, Table 5 and Table 6 of the paper in LaTeX format.
- structure.txt describes the interrelation of program files.
- The folder Synthetic_datasets_for_estimation contains our standard synthetic datasets with known parameter values that can be used to test parameter estimation.
- The folder Synthetic_datasets_for_plotting contains our synthetic datasets that were used to create Figures 1 and 3 of the paper.
- The folder Data_estimates contains results of parameter estimation. These results are reported in Section 6 of the paper.
- The folder Mathematica has a Mathematica (Wolfram Research, Inc.) notebook for calculations in Section 7 of the paper.
- The folder Densityestimation contains:
- densityestimation.m, which estimates the empirical means of the densities of coloured vertices and of adjacent pairs of coloured vertices as a function of lambda (seeding rate) and mu (percolation parameter), for a mesh of lambda and mu pairs, when the number of colours is 1.
- data_visualise.m displays the result of densityestimation.m saved in dataset_A.mat and dataset_B.mat in several plots.
- data_visualise_publication.m creates the figures that are presented in the Appendix of the paper (arXiv:1604.08908v3).
The software in the repository Melykuti/Parameterestimation_MSM is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International Public License. For commercial licensing, please contact Bence Mélykúti.
Copyright (c) 2017, Felix Beck, Bence Mélykúti