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Bayes' unfolding - short recap

The measurement of the $F_2$ structure function is equivalent to the measurement of the differential cross section $\frac{d^2 \sigma}{dy dQ^2}$. Therefore, we need to unfold the measured distribution to get the (``true'') number of the events in the selected bins. Known the $P(E_j\vert C_i)$, the likelihood that effect $E_j$ (an observed event reconstructed in the bin $j$) is due to cause $C_i$, and $n(E_j)$, the measured number of events in the bin $j$, the unfolded number of events due to the $C_i$ is given by:
\hat{n}(C_i) = \frac{1}{ \epsilon_i }\sum_j n(E_j) P(C_i\vert E_j)
\end{displaymath} (1)

where $\epsilon_{i} = \sum_{j=1}^{n_E} P(E_j\vert C_i)$ is the efficiency of detecting an event generated by $C_i$. The elements $P(C_i\vert E_j)$ are calculated by the Bayes' theorem:
P(C_i\vert E_j) = \frac{P(E_j\vert C_i)P_o(C_i)}{\sum_{i=1}^{n_C} P(E_j\vert C_i)P_o(C_i)}
\end{displaymath} (2)

Giulio D'Agostini 2004-05-05