MC_fit_plot

The analysis and filtering of MC_fit results (Fig. 1 and Fig. 2) is done most conveniently using MC_fit_plot. It can also be done manually using spreadsheet software.

MC_fit_plot is available as both a MATLAB script and as a standalone WINDOWS program. The script version provides more flexibility and is recommended if MATLAB is available.

The description below assumes that the best central model has been chosen by minimizing misfit. If the best central model has been chosen to maximize the Bayes score, the same procedure applies, except that the term “misfit” should be replaced with “Bayes score” throughout.

Hint

MATLAB sometimes has difficulties arranging figure panels. To avoid these, maximize the MATLAB figure window before selecting the my_project_central.pts file in Step 1.

The MC_fit_plot user dialog is interactive and relatively straightforward:

  1. Select the my_project_central.pts file of interest. MC_fit_plot automatically finds the corresponding my_project_perturbed.pts file.

  2. Select two inversion parameters of interest, usually pressure and temperature. MC_fit_plot automatically selects misfit as the third variable.

  3. If a subset of the models fit all observational data within analytical uncertainty, a prompt offers to filter the population to include only those models. This prompt does not appear if no or all models fit within uncertainty.

  4. If desired, filter the models by misfit.

  5. The figure generated by MC_fit_plot consists of four panels. The left and right panels show the central and perturbation model coordinates rotated into the plane of the selected inversion parameters. The central panels show the misfit as a function of the selected inversion parameters for the central model analysis. The axes can be rotated or transformed interactively.

  6. Filled symbols represent models that fit all analytical data within its uncertainty. The fit criterion is dependent on the specified confidence interval (uncertainty_multiplier).

  7. One-sigma covariance ellipses are plotted for the best central model and perturbation analysis results.

  8. The misfit of the best central model, \(min(misfit)\), is written to the legend of the left panel, labled simply “misfit”, and the error in the misfit function attributable to analytical and thermodynamic uncertainty, \(\epsilon_{misfit}\), is written to the legend of the right panel.

  9. To compute the total uncertainty on the inversion parameters, run MC_fit_plot a second time filtering (step 4 above) the models by misfit to include only those within \(min(\text{misfit}) \pm \epsilon_{misfit}\). The total uncertainty is then given by the quadrature sum (Eq 5) of the central model and perturbation analysis uncertainties written to the legends of the left and right panels.

  10. MC_fit_plot automatically outputs the plotted figure in bitmap (my_project.png) and vector (my_project.pdf) format. If the figure is modified after the completion of the script, new *.png and *.pdf files can be generated with the MATLAB commands:

    % Export the current figure to my_project.png
exportgraphics(gcf,'my_project.png','ContentType','image','Resolution',300);
% Export the current figure to my_project.pdf
exportgraphics(gcf,'my_project.pdf','ContentType','vector','BackgroundColor','none');