[en] The classical statistics approach used in health physics for the interpretation of measurements is deficient in that it does not allow for the consideration of needle in a haystack effects, where events that are rare in a population are being detected. In fact, this is often the case in health physics measurements, and the false positive fraction is often very large using the prescriptions of classical statistics. Bayesian statistics provides an objective methodology to ensure acceptably small false positive fractions. The authors present the basic methodology and a heuristic discussion. Examples are given using numerically generated and real bioassay data (Tritium). Various analytical models are used to fit the prior probability distribution, in order to test the sensitivity to choice of model. Parametric studies show that the normalized Bayesian decision level k_α-L_c/σ₀, where σ₀ is the measurement uncertainty for zero true amount, is usually in the range from 3 to 5 depending on the true positive rate. Four times σ₀ rather than approximately two times σ₀, as in classical statistics, would often seem a better choice for the decision level