Fit with finite statistics

Joel found this paper, which I think describes exactly what we need. I'm going through it at the moment trying to figure out how to apply it.

There is a root implementation, TFractionFitter, but in one dimension. That could be used by just putting everything in one dimension e.g. instead of a 10x10 bin histogram have a 100 bin histogram. I also found this page which says there are problems with the implementation (although it's unclear for which root version). One of the comments says that there is an implementation in RooFit that works properly though, so I'll have a look at that.

Event selection with TMVA

Link here .

Leptonic event selection update

Today's talk is here.

Leptonic Event Selection

Last week's talk is here.

Correct fits and proposal for more samples

I applied the corrections in the re-scaling of the errors from the templates in the chi^2 function. You can find the results here.

The results in the last column were obtained without taking into account the statistical errors from the templates. We can see that as the number of events increase the absolute value of the errors tend to the case when the errors from the templates are zero. The central values fluctuates a lot. An extra sample with L = 2000 fb^-1 (34000 events of mu-mu-h) would be the minimum (Desch-Kuhl used 5000 fb^-1 and split in data and Monte Carlo) . Presently there is 1000 fb^-1 reconstructed. We can use 500 fb^-1 (which is what one expects in reality) for the data and the other 500 fb^-1 with the extra 2000 fb^-1 that we request. I would prefer more, but we have to see that the time scale is short.

Besides that we should try to get an extra 1000 fb^-1 for likelihood or other method for signal-background separation.

What do you think?

Fit studies

A slide can be found here .

Likelihood fit for Poisson errors

Talk for today is here.

Sorry it doesn't look pretty. The error bar colours are particularly garish.

Muon selection with multivariate analysis

I have the steps to do the muon selection with TMVA more or less documented in my wiki page .

Meeting Minutes and Plans

Today's Meeting Minutes

Attending: Roberval, Hajrah, Mark, Joel

• Mark has been working on the final fitter and showed some plots from pseudo experiments. There are clearly still a few issues to be worked out.
• Roberval and Hajrah have been making good progress on the muon channel. They now use the ROOT package TMVA to perform a multivariate muon selection. They have also been playing around with the fit, including fitting background+gg as a single template.

Preparations for the LOI were discussed. The timescale is short, although uncertain and needs to be checked. The plan is:

1. Roberval will re-visit the event selection, and a common one should be used for the two analyses
2. Mark will continue his fit studies, and the fits from the two channels will be done independently and combined
3. Joel will look at whether the Z-fusion eeH process is an issue.
4. It is uncertain whether combing background+gg templates is the best thing to do, so it will need to be studied

We will have extra meetings in the run up to the LOI, starting next week (at 11:30)

Status of the analysis

Talk can be downloaded from here .

Toy MC fit

I had a quick go at a toy MC fit, needs a bit more work though.

First I created two toy data sets from the Poisson distribution of some input histograms, and then tried fitting them together using the error on both to calculate the chi2. First results are here. The gluon fit seems to be a bit erratic for some reason.

I then tried fitting one of the toy sets to the input using only the error on one of them. The results are here. Something's clearly going wrong here, I'm looking in to it but probably won't have time before the meeting at 11. The results are so bad it's got to be something obvious though.

In both sets of plots the black line is the true value of the ratio.