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Brían
I hijacked the newly created KM3NeT-Nikhef reco git repository,
to formulate some action points surrounding the track reconstruction.
Please feel free to comment and contribute.
Bouke: No need to call it hijacking. The git repository was set up for all of us to contribute and work together. So by all means make use of it!
Valentin
Looking further into the discrepancy between the JGandalf track lengths and the MC-truth.
One of the things I struggle with at the moment, is that I do not have access to the track length in the reconstructed files we are using for this study.
Maarten: These are probably not written to the output at the moment. We should look into it.
More generally, we should create something to study the module response (on hit level).
Thijs
Jacobians which translate JPP parameters to fit parameters are currently still missing.
If we want to get the derivatives with respect to the direction parameters (instead of the vertex position parameters), then we end up with derivatives like dy/dz and dx/dz. How can these be used as direction cosines?
Maarten: As long as the directional changes are small (assuming you start value is close to the actual direction), this is okay. Thereby we can also immediately assume that the orientation of the PMT does not change much.
Rotating the z-axis along the shower-direction has many advantages (x-value becomes distance between shower and PMT, etc.). May even allow a big speed-up later, if we use implement theta0 directly as the angle of emission.
In addition, here does dcos(theta0)/(d(dx/dz)) = -xz^2 / D / R come from?
Maarten: Not entirely sure this is correct. Please check it. Start from the geometrical picture and (re)derive algebraically.
Some discussion ensued about the generality of the current reconstruction algorithms, the shape of the likelihood landscapes:
Ronald: I assumed that the problem you were struggling with is how you go to the unrotated reference frame. If that's the case the first thing you need to do is to write down all the rotation formulas and then take the derivative there.
Maarten: No. The first thing you do is rotate your shower along the z-axis. Then you do the fit. Then you have to rotate the whole system back. The tricky thing is just in which coordinates you want the error matrix of your fit parameters to be defined.
Since lengths are preserved in the rotations, so the errors should not be affected.
What I find truly important, is that the direction cosines become truly orthogonal when you rotate into the shower direction.Ronald: The start direction and the real fit direction being close enough together may not always be the case. So this is not a fully general solution. I was wondering whether Thijs and Brían are not struggling with the general scenario (i.e. the start value not being close enough).
Suppose you have a nice parabolic likelihood landscape and you start very far away from the minimum, how can you do the MLE using the method discussed above?Maarten: What this method is meant for here of course, is minimizing the local likelihood landscape.
Ronald: Can we not consider the general solution?
Maarten: This might be interesting from a scholarly perspective. But very hard practically.
Ronald: But we should not limit ourselves to the current reconstruction philosophies only.
We may for example want to consider PDFs which are less dependent on the assumptions that we make at the moment (such as the assumption that the prefit yields a direction close to the real direction).
Finally, there was some discussion on the minimizer and the statistical inference used in general:
Jordan: We should try to set up some mechanism to evaluate different minimizers and reconstruction procedures.
Maarten: The minimizer always finds a local minimum and the error matrix tells you about the uncertainty on this minimum (how wide the minimum is).
However, the direction likelihood landscape is really really difficult to evaluate (if you cross from one side of a module to the other side, you run into poles, etc.).
We should invest time and effort into making the PDFs more easily evaluable.Ronald: In addition, we should try Bayesian methods, instead of the Markov chains that are currently in place.