Probabilistic assessment for a sample to be radioactive or not: application to radioxenon analysis

When a net count value is below the type 1 error critical limit it is customary to declare that the activity is “below the detection limit”. The content of this declaration is particularly impoverished, incapable for example of discriminating between a net measurement just below the critical limit, but positive, and a negative net measurement, two types of information that it is legitimate and intuitive to think do not have the same weight of information. In the case of a spectral measurement of ^131mXe and ^133mXe certain information is available according to the various X and gamma emissions, which might all be below their respective critical limits. We shall see that a Bayesian probabilistic approach can be used, without considering the critical limits, to obtain anti-correlated maximum likelihood values taking all the information into account jointly and to obtain powerful and pertinent information in the form of the absolute probability that the sample contains ^131mXe and/or ^133mXe, all possible activity values combined. Conversely, of course, this is used immediately to deduce the probability that the sample does not contain ^131mXe and/or ^133mXe. This information enables the customary critical limit to be ignored.