Add empirical coverage diagnostic plots

[lasse-meixner]

Resolves #577.

Description

Creates coverage plots showing empirical coverage of posterior credible intervals.
A well-calibrated model would have coverage exactly match interval width (i.e. 95% credible interval contains the true value 95% of the time) as shown by a diagonal line.

The coverage for the provided simulated datasets is accompanied by credible intervals for coverage proportion (in form of a gray ribbon). These are calculated via the standard (conjugate) Beta-Binomial model for binomial proportions with a uniform prior.

Changes

• adds module bayesflow.diagnostics.plots.coverage implementing coverage plot and coverage diff plot
• adds auxiliary function compute_empirical_coverage in bayesflow.utils.plot_utils

Example
Here an example of a model that is "too uncertain", or too conservative. It over-covers:

[stefanradev93]

Hi Lasse, I agree that this would be a very nice feature (which we implicitly care about when we compute the expected calibration error / ECE metric). And thank you for the PR, which I will review asap.

[stefanradev93]

Hi Lasse, thanks for the PR and for following all contribution guidelines! I think the PR is almost merge-ready up to a small discussion on the following point:

• Since the two new functions coverage and coverage_diff share a lot of code and logic, I wonder if it would make sense to merge them into a single function with an optional difference boolean flag, akin to what we have for the ECDF plots?

Also, do you happen to have a reference for the beta formulation of the coverage confidence bands which we can include in the docstring?

[lasse-meixner]

@stefanradev93 sure!
I agree with your first point, I merged the two as suggested. Regarding a source for the beta-binomial model I added a docstring reference to Chapter 2 of `Bayesian Data Analysis (2013, 3rd ed.) by Gelman A., et al. where this is covered.

[codecov]

Codecov Report

❌ Patch coverage is 93.58974% with 5 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
bayesflow/utils/plot_utils.py	89.18%	4 Missing ⚠️
bayesflow/diagnostics/plots/coverage.py	97.50%	1 Missing ⚠️

Files with missing lines	Coverage Δ
bayesflow/diagnostics/plots/__init__.py	100.00% <100.00%> (ø)
bayesflow/utils/__init__.py	100.00% <ø> (ø)
bayesflow/diagnostics/plots/coverage.py	97.50% <97.50%> (ø)
bayesflow/utils/plot_utils.py	76.47% <89.18%> (+3.53%)	⬆️

... and 5 files with indirect coverage changes