Probabilistic assessment for a sample to be radioactive or not: application to radioxenon analysis
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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.
KeywordsBayesian statistic Radioxenon X and gamma spectrometry Metastable radioactive isotopes of xenon Critical limit