U.S. Department Of Energy's nuclear engineering education research: highlights of recent and current research-III. 6. Bayesian Methods for Radiation Dosimetry

Bayesian methods have the advantage that uncertainty about quantities of interest is described with the help of probability densities. This fact makes it possible to use probability calculus to concatenate probability statements and derive probabilities for related quantities of interest 'coherently'. Here, we discuss the application of Bayesian methods to calibration for external dosimetry and to compartmental analysis for internal radiation dosimetry. We derived the calibration density for chromosome aberration data with imprecise radiation doses to describe the uncertainty of the neutron dose received by an individual with observed dicentric chromosome aberrations. For compartmental analysis, we derived the posterior densities, expectations, and standard deviations of the models' transfer rates and time-dependent expectations and standard deviations for the 45Ca activity in a bone surface compartment. We graphed and compared the calibration density for 143 observed dicentric aberrations in 128 cells for precise and imprecise doses and found greater variance for the unknown dose df for the case of imprecise calibration doses, as expected. In internal dosimetry, we derived the posterior densities, expectations, and standard deviations for the parameters of the compartmental model and predicted the time-dependent expectations and standard deviations for bone surface activities. Three-dimensional numerical integration yielded the following estimates for the transfer rates: ρ = 0.025 ± 0.021, σ = 0.021 ± 0.017, and τ = 0.006 ± 0.004. The expected bone surface activities (± standard deviation) at times 11, 60, 240, and 510 min after intake are 3.50±1.82, 7.70±1.48, 6.41±0.68, and 3.73± 0.72. These values are in good agreement with the observed activity values