Abstract An important component of protecting individuals from the hazards of radiation exposure is to be able to determine whether radionuclides have been taken into the body, and in what quantities. For example, a urine sample from an individual who works with plutonium can be analyzed by α spectroscopy or mass spectroscopy to determine if plutonium is present in the sample, and hence to make an inference about possible plutonium intakes in the individual's history. Often, the quantities of plutonium that one seeks to detect are comparable to the measurement uncertainties. Hence, statistical considerations are a very important aspect of the detection methodology.