Keep negative entries by default. Solves #119.

[fzeiser]

Keep negative entries in Ensemble, Unfolder and Fristgen by default.
With this, we may avoid a bias due to removal of negative counts, see #119.

[fzeiser]

Unfortunately, this doesn't quite seem to work! The implementation is ok, and running it on the "normal" 164Dy dataset is fine. However, on the dataset with reduced statistics and the artificial dataset (RAINIER), I get a problem. Here some more details.

The initial_guess for the nld normalization is quite wrong/off for some ensemble members. Thus the normalization with MultiNest will be off, too. I tried to see whether this is a bug in the implementation, so I had a look at the ensemble members themselves:

Here you can see with the faint grey lines, that some members (here only one, but not many ensemble members in total here) show a strong dip in the NLD at high energies. This is quite unexpected - whereas the dip at low energies could be well explained by the absence of levels in that region.

So I had a look at the first generation matrix of an ensemble member that has this dip. Here is the "problematic" member:

And the fg and fit; Upper pannel: ensemble_fg, lower pannel: fit to it:

In addition a projection of 200 keV wide bins for several excitation energies:

I think we see the problem here: For an overall reproduction of the first-generation spectra, we get some bins with quite a large number of negative counts....

Now what is the total impact: If we were able to specify the uncertainty of the datapoints in advance of the fitting of the nld, this issue here should not be a problem. However, in the current implementation we assume that we cannot get the uncertainty in advance*, and specify a relative uncertainty of 0.3*value for each bin. Thus, if we get a dip in the high energy part of the nld, this will lead have a very very high impact on the T parameter :/. Which we know is unreasonable, because this point was just off.

Note: For this dataset, with RAINIER, we have an additional "problem" with the nld point at Ecrit=1.3 MeV. Due to the same type of specification, it may lead to weird results.

For now, I don't think that we are able to "fix" this problem.

*Note: One could also try to transform all ensemble members in such a way as to minimize the sum of difference between each bin. This ensemble of transformed members could be a good representation of the mean.

[fzeiser]

A little more explanation on the through about the transformed ensemble members. The original problem about using the mean of the extracted nld and gsf is that they may all have different transformations. Thus the mean and std will capture both the statistical variations and the difference due to the (arb.) transformations.

If we now first find a transformation for each ensemble member such that the difference to a reference (eg. member no. 0) is minimized, we should get rid of the differences due to arb. transformations. Then we might use the mean and std. directly, or inform the normalization of each member with the std. deviation from the mean. The latter case has the advantage that we easily keep the correlations between different ndl&gsf combinations.