Gauss versus Poisson statistics; what can we learn from Binned and Unbinned fitting of toy Monte Carlos

by Prof. Ulrich Schmidt (Uni Heidelberg)

Thursday Nov 28, 2024, 9:30 AM → 10:30 AM Europe/Berlin

E18/ENE Seminar Room 3268 (TUM PH)

Starting point of these investigations was the benchmarking of unbinned and binned fitting methods using toy Monte Carlos. The special model I used, was double exponential decay and the Monte Carlo data sets had “high” statistics, typically $10^5$ events per data set. The unbinned fitting results always revealed the parameters I put into the toy Monte Carlos. After binning the data set I used Neymann-LeastSquare and Parson-LeastSquare to fit the data sets. Both methods show some systematic bias of the fit results, much higher than I expected. Switching to the L-LeastSquare method, which I will explain in more detail, removes the bias of the fit parameter. Nevertheless the minima of the L-LeastSquares were no longer $\chi^2$-distributed, so this quality of fit measure fails. I will discuss my approach to fix this problem.