Interpretation of the measurement results near the detection limit in gamma-ray spectrometry using Bayesian statistics

The requirement that the true value of an activity cannot be negative is used for the transformation of raw observed values, which can be positive or negative, into the expected activity values. The probability distribution of the activity values is a truncated Gaussian distribution, and the expected value and the variance of the activity values are derived from the observed value and its standard deviation. It has been shown that the standard deviation of the activity values is smaller than the standard deviation of the observed value and that the ratio of the standard deviation of the activity values and the expected value is less than unity. Since the expected activity value is larger than the original observed value, and the standard deviation of the activity values is smaller than the standard deviation of the observed value, the additional information, that the activity cannot be negative, leads to an improvement in the result. However, since the expected activity value depends on the standard deviation of the observed value, conservatively assessed standard deviation lead to a bias of the expected activity values.