Title: Detection of the Short-lived 222Rn-Daughter Products
The traditional approaches to 222Rn-daughter detection use the Bateman equations (BE) for radioactive series decay to arrive at estimates of the airborne concentrations of the short-lived daughter products of 222Rn. This works quite well for high concentrations since the description of average behavior provided by the BE is then adequate. At low concentrations the stochastity of the sampling and the decay processes becomes important. We are using the stochastic processes to estimate the unknown airborne concentrations. The estimated concentrations are given in the form of probability densities which describe the remaining uncertainty about the unknown concentrations.
Title: Bayesian Techniques for the Imputation of Missing Radiation Monitoring Data
Occupational radiation exposure records are often incomplete. Epidemiologic analyses of data require complete radiation monitoring information for the biostatistical methods to be applicable. We developed Bayesian techniques using normal and hybrid log-normal models to input missing data. The hybrid log-normal is characterized by three parameters for the mean, variance and for the predominance of normal or log-normal behavior. Using numerical integration techniques, we were able to obtain the posterior distributions for all parameters and the predictive distribution for a future observation.
Title: Estimation of Radionuclide Retention Parameters and Prediction of Retention Functions
We are developing Bayesian techniques to estimate the parameters of the retention functions for several radionuclides using multiresponse data (e.g., data on retention and excretion). Predictive distributions are used to determine the retention function at times different from the times of the observations of the retention. So far we have used data on the retention and excretion of 226Ra to estimate the parameters for different retention models. The retention functions considered up to this point are: the Norris retention function and this function modified by an exponential term. We found great variations in parameter estimates for different individuals.
Title: Comparative Toxicity of Ionizing Radiations
We are analyzing a data set from Oak Ridge National Laboratory on radiation carcinogenesis in mice exposed to neutron and gamma radiation to determine the RBE for neutrons. The remaining uncertainty about the RBE is characterized by a probability density. We are also investigating dependence of competing risks as one particular source for RBE uncertainty. So far we have used two different ways to construct bivariate distribution functions with different degrees of statistical dependence. One construction method was invented by Morgenstern (Comm. Stat. 4(5), 415-427 (1975)). It yields bivariate distributions with given marginal distributions. Since it seems to yield mathematically more tractable forms, we are focusing on this method to obtain a bivariate distribution with Weibull marginals.
We are also analyzing data sets on the comparative toxicity of 239Pu and 226Ra in beagles. The approach uses the same techniques described above.