Confidence level definition issue for higher dimensions #2
Description
The argument confidence_levels of the Fitter class handles either confidence levels as a percentage or as sigma levels if use_sigma_confidence=True. In the latter case the confidence levels are calculated as the corresponding confidence of a 1D Gaussian. This is a convenience feature to get exact confidence levels for 1-3 sigma (68%, 95%, 99.7%) that are frequently used. If sigma levels are used as input, the plot functions in plot.py label the confidence regions as X sigma. This is incorrect and causes confusion for 2D plots, since an input of confidence_levels=[1,2] to Fitter means internally that the confidence regions for 68% and 95% confidence are calculated and marks them as 1 and 2 sigma in the plot. But for a 2D gaussian this does not correspond to the 1 and 2 sigma levels, which are only 39% and (don't know the exact other value). The internal calculation for the actually assumed 68% and 95% confidence is correct!
- Find better less confusing way of passing input
- Fix the output labeling
- Does it make sense to use sigma levels of 1D gaussian?
- Even if labeled correctly, setting 68% confidence regions for a 2D gaussian is unusual