Bayesian hypothesis testing-use in interpretation of measurements.

Bayesian hypothesis testing may be used to qualitatively interpret a dataset as indicating something "detected" or not. Hypothesis testing is shown to be equivalent to testing the posterior distribution for positive true amounts by redefining the prior to be a mixture of the original prior and a delta-function component at 0 representing the null hypothesis that nothing is truly present. The hypothesis-testing interpretation of the data is based on the posterior probability of the usual modeling hypothesis relative to the null hypothesis. Real numerical examples are given and discussed, including the distribution of the non-null hypothesis probability over 4,000 internal dosimetry cases. Currently used comparable methods based on classical statistics are discussed.