Reporting gamma-ray spectrometric measurement results near the natural limit: primary measurement results,best estimates calculated with the Bayesian posterior and best estimates calculated with the probability density distribution resembling shifting

When reporting best estimates as measurement results, systematic influences near the natural limit are introduced that originate not only in the possible inconsistency of the analytical procedure but also in the conversion of the primary measurement results to best estimates. It has been shown that the probability density distribution resembling shifting of values observed in the unfeasible region to the limit of the feasible range (the natural limit) introduces a smaller systematic influence than the Bayesian posterior, resembling censoring with repetition of the measurements that result in observed values in the unfeasible region. The drawback that the uncertainty intervals calculated with the Bayesian posterior do not encompass the natural limit and may not encompass the observed value, although it lies within the feasible region, is avoided by using the probability density distribution resembling shifting. Therefore, such best estimates introduce a smaller systematic influence into the measurement results and are better suited as inputs for subsequent analyses.