Unfolding

On the following pages I would like to give you a short summary why unfolding is very important when analysing data.

In order to learn something about nature experimentally, knowledge about the distribution f(x) of some physical quantity (such as e.g. the energy of a particle) has to be gained. This function f(x) can then be used to test theoretical models or to determine the parameters in a model.

However, we have to perform a measurement which complicates things by mainly three effects:

• Acceptance: An ideal detector would respond to every event, real detectors may not because e.g. some time is needed after a measurement has been made to reset the detector, the detector may be ``blind'' in some regions of x (i.e. some values of x cannot be measured with this detector at all), etc. Thus, the detector acceptance (i.e. the probability to observe a given event) is less than one.
• Resolution: In an ideal world, our detector would measure the event with infinite accuracy, i.e. the measured value would be identical to the true value. Unfortunately, measured quantities are smeared out in our detector due to finite resolution. Thus, there is only a statistical relation between the true value and the measured value.
• Transformation: So far we considered only the direct measurement of a true variable x, i.e. if we neglect problems due to resolution and acceptance for the moment, our measured value is identical to the true value we are interested in. However, many physical properties we are interested in are not accessible experimentally. Instead we have to measure quantities which maybe (only weakly) correlated to the quantity of interest. Furthermore, even if the quantity of interest is accessible experimentally, the detector may distort the measured quantity, e.g. by a constant shift, etc. This behaviour is also known as ``bin-to-bin migration'' (if all quantities are binned into histograms)

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