The $C(PhP)$

One of the cause that contributes to the $F_2$ measurement is the so called photoproduction background, generated according the 3 in the low $Q^2$ regime (the average value is $\sim 10^{-5}$). This cause is included in the unfolding procedure. Therefore if $N$ were the selected bins to extract the $F_2$ values, the all cause's cells are now $N +1$. But Bayes' theorem requires the knowledge of initial probability $P_o({\bf C})$. These $P_o({\bf C})$ represents the relative normalisation among the different causes, so they should be chosen in agreement with the cross section for each cause ¹. The initial value is estimated by Monte Carlo simulation based on PYTHIA [4], with the MRSA [5] structure function. The used sample corresponds to an integrated luminosity ${\cal L}_{php} = 253.1$ nb$^{-1}$. At this level we are in the same condition of the standard method: we use as input value the number given by the Monte Carlo, the same value that are subtracted in the standard approach. Anyway, this is just an initial condition, after the unfolding, in fact, we get the (``true'') $P_o({\bf C})$ according to the data. This is the reason why the Bayes unfolding allows to infer from the data not only the $F_2$ values but also important informations related to the background sources.