Bayesian internal dosimetry calculations using Markov Chain Monte Carlo.

A new numerical method for solving the inverse problem of internal dosimetry is described. The new method uses Markov Chain Monte Carlo and the Metropolis algorithm. Multiple intake amounts, biokinetic types, and times of intake are determined from bioassay data by integrating over the Bayesian posterior distribution. The method appears definitive, but its application requires a large amount of computing time.

Bayesian prior probability distributions for internal dosimetry.

The problem of choosing a prior distribution for the Bayesian interpretation of measurements (specifically internal dosimetry measurements) is considered using a theoretical analysis and by examining historical tritium and plutonium urine bioassay data from Los Alamos. Two models for the prior probability distribution are proposed: (1) the log-normal distribution, when there is some additional information to determine the scale of the true result, and (2) the 'alpha' distribution (a simplified variant of the gamma distribution) when there is not. These models have been incorporated into version 3 of the Bayesian internal dosimetry code in use at Los Alamos (downloadable from our web site). Plutonium internal dosimetry at Los Alamos is now being done using prior probability distribution parameters determined self-consistently from population averages of Los Alamos data.

Analyzing bioassay data using Bayesian methods--a primer.

The classical statistics approach used in health physics for the interpretation of measurements is deficient in that it does not take into account "needle in a haystack" effects, that is, correct identification of events that are rare in a population. This is often the case in health physics measurements, and the false positive fraction (the fraction of results measuring positive that are actually zero) is often very large using the prescriptions of classical statistics. Bayesian statistics provides a methodology to minimize the number of incorrect decisions (wrong calls): false positives and false negatives. We present the basic method and a heuristic discussion. Examples are given using numerically generated and real bioassay data for 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 for typical situations involving rare events the normalized Bayesian decision level k(alpha) = Lc/sigma0, where sigma0 is the measurement uncertainty for zero true amount, is in the range of 3 to 5 depending on the true positive rate. Four times sigma0 rather than approximately two times sigma0, as in classical statistics, would seem a better choice for the decision level in these situations.