[en] The authors discuss an internal dosimetry problem, where measurements of plutonium in urine are used to calculate radiation doses. The authors have developed an algorithm using the MAXENT method. The method gives reasonable results, however the role of the entropy prior distribution is to effectively fit the urine data using intakes occurring close in time to each measured urine result, which is unrealistic. A better approximation for the actual prior is the log-normal distribution; however, with the log-normal distribution another calculational approach must be used. Instead of calculating the most probable values, they turn to calculating expectation values directly from the posterior probability, which is feasible for a small number of intakes

[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

[en] New methods for the inverse problem of internal dosimetry are proposed based on evaluating expectations of the Bayesian posterior probability distribution of intake amounts, given bioassay measurements. These expectation integrals are normally of very high dimension and hence impractical to use. However, the expectations can be algebraically transformed into a sum of terms representing different numbers of intakes, with a Poisson distribution of the number of intakes. This sum often rapidly converges, when the average number of intakes for a population is small. A simplified algorithm using data unfolding is described (UF code). (author)

[en] 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 dosimetric 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. (author)

[en] A new internal dosimetry code for interpreting urinalysis data in terms of radionuclide intakes is described for the case of plutonium. The mathematical method is to maximise the Bayesian posterior probability using an entropy function as the prior probability distribution. A software package (MEMSYS) developed for image reconstruction is used. Some advantages of the new code are that it ensures positive calculated dose, it smooths out fluctuating data, and it provides an estimate of the propagated uncertainty in the calculated doses. (author)

[en] 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. The authors 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_α = L_c/σ₀, where σ₀ is the measurement uncertainty for zero true amount, is in the range of 3 to 5 depending on the true positive rate. Four times σ₀ rather than approximately two times σ₀, as in classical statistics, would seem a better choice for the decision level in these situations

[en] Internal dosimetry may be divided into tow main problems: (1) the forward (scientific) problem of determining biokinetics models that describe how radionuclides are taken into the body, distributed in body tissues, and excreted, and (2) the inverse (mathematical) problem: given the measured amounts in excreta and assuming a biokinetic model, to determine the times and amounts of intakes into the body. The inverse problem of internal dosimetry is, in fact, a generic problem studied in other fields (e.g., image reconstruction, spectral deconvulution, and model parameter fitting). We have developed a code for plutonium internal dosimetry using the maximum entropy method, a method for solving underdetermined inverse problems with a positivity constraint. Within the framework of Bayesian statistics, we believe the definitive approach is to examine the Bayesian posterior probability describing the probability of an intake scenario (X_i) read ( ... ) as open-quotes the set of,close quotes where X_i denotes the intake amount that occurs on the with day. For plutonium, for a worker with a long employment history, this is a very high dimensional probability space, since there may be on the order of 10,000 days when intakes may have occurred. Within this high dimensional space, we calculate the mean intake scenario as < X_i> where < ... > denotes the expectation value over the posterior probability distribution. Similarly, we calculate uncertainties and other relevant quantities, such as X², as expectation values over the posterior distribution. Thanks to a recent breakthrough in describing the mathematical structure of the intake process (a Poisson sum representation of intakes), we have developed the initial version of a Bayesian expectation-value algorithm for internal dosimetry reconstructions

[en] The internal dosimetry program at Los Alamos National Laboratory uses applications of Bayesian statistics in the estimation of intake dates and quantities, and associated committed doses from inhalation of ²³⁹Pu. The construction of prior distributions, based on urine bioassay results from populations of plutonium workers, has reemphasized the fact that current radiochemical techniques using α-spectroscopy do not provide detection limits that meet DOE regulations (i.e., detection of intakes resulting in a committed effective dose of 1 m Sv in the year of intake). We are in the process of constructing a bioassay analysis regimen that uses thermal ionization mass spectrometry in conjunction with α-spectrometry to optimize detection of intakes in a cost effective manner. The mass spectrometry system at Los Alamos has a detection limit of 7 gBq L^-1 for ²³⁹Pu in urine compared to 2 n-Bq L^-1 from classical radiometric methods. Results are used to construct prior distributions for worker and non-worker populations. The improved sensitivity, combined with the decision making capabilities of the Bayesian framework, provides a powerful method for detecting intakes in both plutonium workers and non-occupational populations

[en] Classically, the mean and variance of radioactivity measurements are estimated from poisson distributions. However, the random distribution of observed events is not poisson when the half-life is short compared with the interval of observation or when more than one event can be associated with a single initial atom. Procedures were developed to estimate the mean and variance of single measurements of serial radioactive processes. Results revealed that observations from the three consecutive alpha emissions beginning with ²²²Rn are positively correlated. Since the poisson estimator ignores covariance terms, it underestimates the true variance of the measurement. The reverse is true for mixtures of radon daughters only. (author)

[en] The application of Bayesian statistical methods to the interpretation of radiation protection measurements has been discussed in the first article of the series in 1993. The present work continues that discussion and (1) provides sharper definitions of detection categories POSITIVE, SMALL, and NDA; (2) describes an empirical method for determining the prior probability distribution; (3) describes a sequential re-measurement strategy; and (4) defines detection limits L_MDA (minimum detectable amount) and L_MMA (maximum missed amount) based on the Bayesian detection criterion POSITIVE. It is shown that the Bayesian detection criterion is always more stringent than the classical criterion. (author)