Software 99-007

In the following, some guidelines for a consistent performance evaluation
are collected.

A second ingredient is the geometrical range of the detector. It does
not make sense to judge the performance of a reconstruction program on
tracks which which are outside the acceptance of the detector, or just
straddling its border. Objects of interest within the geometrical acceptance
region define the *reference set*.

In many cases, the geometrical criterion can be conveniently defined
by the number of detector elements, eg. the number of layers in a tracking
system, which have been passed by the particle, which can be derived from
the *Monte Carlo Impact Points (MIMPs)* provided by the detector simulation.
Example: for the vertex detector, tracks within the acceptance region pass
at least three superlayers. Assuming that each superlayer has four logical
GEDE planes on two detector modules per quadrant, giving rise to two MIMPs
per superlayer, a requirement of at least 6 MIMPs for a reference particle
may be appropriate. It is permissible to discard MIMPs outside the sensitive
region from this count but it should be stated.

ewhich is independent of the hit efficiencies of the individual detectors. Since the definition of the reference set has potential influence on the reconstruction efficiency, the corresponding geometrical acceptance should always be considered as well.^{X}_{geo}= N^{X}_{ref}/ N^{X}_{tot}

Parameter matching is sometimes the only way because it requires not direct Monte Carlo relation information between generated particle and the detector hits used in the reconstruction. In high particle densities however, it bears the danger to accept random coincidences between Monte Carlo particles and ghost reconstructions and can lead to the paradox impression that the reconstruction efficiency

- parameter matching
- hit matching

The recommended technique for HERA-B is therefore based on hit matching:
the reconstructed track is *assigned* to the Monte Carlo particle
which contributes the largest fraction of its hits if this fraction exceeds
a certain limit. The contribution fraction of a Monte Carlo particle *m
*is defined as

fwhere N_{m}= N^{m}_{hits}/ N_{hits}

The track is assigned to the particle of largest contributed fraction
if it exceeds a lower limit f_{min}. A typical choice for tracking
applications is f_{min}=70%.

A particle is called reconstructed if at least one reconstructed object
is assigned to it. The reconstruction efficiency is then

e = Nie. the fraction of reference tracks which are reconstructed._{ref}^{reco}/ N_{ref}

A ghost rate can be defined as

eIt is informative to also provide the mean number of ghosts per event._{gh}= N_{ghost}/ N_{ref}

Nand one can define the_{m}^{clone}= N_{m}^{reco}- 1 , if N_{m}^{reco}>0

0 , otherwise

e_{clone}= N^{clone}/ N_{ref}

The quality of the parameter estimate is reflected in the parameter
residual

R(Xwhere X_{i}) = X_{i}^{REC}-X_{i}^{MC}

If the reconstruction tool provides also an estimate of the parameter
covariance matrix (C_{ij}), it is very informative to investigate
the *normalized parameter residual* or *pull*, which is defined
as

P(XIdeally, the pull should follow a Gaussian with mean value zero and standard deviation one._{i}) = (X_{i}^{REC}-X_{i}^{MC}) / (C_{ii})^{1/2}