The LDETECT and MDETECT algorithms calculate a quantity for the significance of the source detection called SNR which comes from the term Signal-to-Noise Ratio, which unfortunately is a misleading nomenclature. Actually it is the source existence likelihood and is defined as
where P is the probability that the observed distribution
of photons originates from a spurious background fluctuation
which in turn is calculated from Poisson statistics.
Which threshold one wants to set for a significant detection of
a source depends on how many spurious sources one wants to accept
in a sample and in turn, how many trials one has made.
The number of statistically independent trials made in the different
detect algorithms can usually only be estimated by extended simulations.
As an example we
[Hasinger and Hartner]
have tested the standard analysis combination of LDETEC and MDETEC
on several hundreds of artificial empty PSPC fields
(512 
512 images, pixel size 15") of variing exposure time
and came to the conclusion that about 16000 and 50000 independent trials
are made for each run of LDETECT and MDETECT, respectively,
most of them in the inner part of the PSPC field of view (FOV).
As an example, a likelihood of 10 corresponds to a chance probability
of 
, so that one expects about 0.7 and 2.3 spurious
sources per PSPC FOV in LDETECT and MDETECT.
In the standard analysis scheme LDETECT and MDETECT are, however, not meant to set the final thresholds, but only to provide the input for the background map calculation and to filter the positive excesses in the image (which could be possible sources) for assessment by the more sensitive Maximum Likelihood Algorithm (ML). Therefore we advise to set the thresholds in the binned detect procedures to a lower value (e.g. 8) in order to ensure completeness as far as possible.
The ML-algorithm calculates a similar significance criterion through a Likelihood Ratio Test, as e.g. in [Cash1979, Cruddace et al.1988]:
where L(S) is the likelihood to find the measured distribution of photons under the assumption of a source of strength S being present and L(0) is the likelihood to find the same distribution from pure background. The quantity ML should follow a chi-square distribution with N degrees of freedom, where N is the number of statistically independent parameters. In the case of N = 1 the expected distribution of ML is again an exponential:
Given the complexity of the SASS/EXSAS detection procedure it is practically impossible to analytically predict the expected probability distribution of ML, so that an empirical calibration is necessary. At a very early stage in the preparation of the ROSAT mission (1988) we simulated hundreds of empty PSPC fields (see above) and came to the conclusion that about 1500 trials are performed in the inner 20' radius PSPC field (assuming an exponential distribution of ML), however, the number of trials here is strongly depending on the previous history of LDETECT and MDETECT runs. In the meantime the ML algorithm has been substantially improved and in particular runs in several energy bands simultaneously, so that the effective number of trials will be larger. As a conservative threshold we therefore propose ML = 10, but suggest to the critical user to perform his own assessment of the likelihood distribution, e.g. by simulations or bootstrapping.