Changes between Version 12 and Version 13 of DatabaseBasedAnalysis/Spectrum

Timestamp:

Dec 3, 2019, 5:02:01 PM (10 months ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -7 +7 @@
 
 For an observation with an effective observation time \(\Delta T\), this yields:
-\[\phi(E) = \frac{1}{A_0\cdot \Delta T}\frac{dN}{\epsilon(E)\cdot dE}\]
+\[\phi(E) = \frac{1}{A_0\cdot \Delta T}\frac{dN}{d\epsilon(E)\cdot dE}\]
 
-The total area \(A_0\) and the corresponding efficiency \(\epsilon(E)\) are of course only available for simulated data. For simulated data, \(A_0\) is the production area and \(\epsilon(E)\) the corresponding energy dependent efficiency of the analysis chain.
+The total area \(A_0\) and the corresponding efficiency \(\epsilon(E)\) are of course only available for simulated data. For simulated data, \(A_0\) is the production area and \(\epsilon(E)\) the corresponding energy dependent efficiency of the analysis chain. For a given energy bin, the efficiency is then defined as 
+
+\[\epsilon(E) = \frac{N_\textrm{exc}(E)}{N_0(E)} \]
+
+where \(N_0\) is the number of simulated events in this energy bin and \(N_{exc}\) the number of *excess* events that are produced by the analysis chain.
+
+The number of excess events, for data and simulations, is defined as
+
+\[N_\textrm{exc} = N_\textrm{sig} - N_\textrm{bg}\]
+
+where \{N_\textrm{sig}\) is the number of events identified as potential gammas from the source direction ('on-source') and \(N_\textrm{bg}\) the number of gamma-like events measured 'off-source'. Note that for Simulations, \(N_\textrm{bg}\) is not necessarily zero for wobble-mode observations as an event can survive the analysis for on- and off-events, if this is not protected by the analysis chain.