Simulation Copula

This repo contains different script used to investigate on hypothesis concerning copulas applied to imprecise probabilities.

Here is a small sum up of the different scripts:

• copulas.py simple script containing the definitions for the different copulas considered
• necessity_functions.py contains different objects for defining univariate and bivariate necessity functions (with mass etc...)
• robust_set_sampling.py contains different object for defining and computing the lower envelope of "robust" credal sets (both univariate and bivariate).
• ordering_focal_set_importance.py script that generate both "mass" and "robust" credal sets with all orders on focal sets, for all marginals in a given range. Does the sampling of marginals incrementally (not optimal but goes to all extremes). Outputs a dataframe that indicates the orders on focal set where the robust set is a subset of the mass set.
• random_ordering_focal_set_importance.py same as ordering_focal_set_importance.py but the sampling is random (with seeding)

And the different notebooks:

• Copulas.ipynb basic notebook to do some test and some verifications. Not interesting
• dataframe_analysis.ipynb Plot figures to visualize marginal necessities and index processing to be sure that we consider the same marginals when comparing different copulas.

Requirements

pandas>=1.2.0 for using pd.DataFrame.merge(df, how='cross')