Example 3 Frequentist studies
These are both toy examples meant only to instruct on statistics, not based on any real data.
WIP notes.
Lets define X^2(dat, pred) = (dat-pred)^2/pred. Lets say Hlee is the LEE hypothesis and Hbkg is the background only hypothesis. If a hypothesis has a prime (') it means its a draw from that distribution (either by poission statistics or covariance sampling so H'lee and H'bkg).
To exclude the LEE we generate fake data under both hypothesis Plee = PDF(X^2(H'lee,Hlee)|Hlee) and Pbkg = PDF(X^2(H'bkg,Hlee) |Hbkg).
Similar to example 2, for example 3 to work one must have already successfully ran example 1. To run with 40k (default) MC poission sampled fake data spectra only:
./example3 --xml example.xml -n 40000
To run with sampling from the calculated covariance matrix:
./example3 --xml example.xml --covariance -n 40000
Note: Sampling from the covariance matrix was added from a forked branch just yesterday and testing is underway to ensure everything is working, so treat this as preliminary functionality at the moment.
Currently this example generates PDF distributions for the case of excluding the LEE hypothesis and shows the power, significance and CLs of the test for a variety of possible points, assuming the bkg model is true (this plot is representative, not necessarily 100% identical to what you will get)
