Calibrative Densities for Radiation Dosimeters

We derive calibrative densities p(df|D) for the unknown 'future' dose df to a dosimeter for two sets of calibration data, Dc. The two sets of calibration data are for film and thermoluminescent dosimeters (TLDs). The p(df|D)s describe the remaining uncertainty about df conditional on D = {Dc, yf.}. The calibration data Dc for the film dosimeters consist of pairs {di, yi}, where di is a radiation dose and yi is an optical density interval. In the case of the TLDs the pairs are {di, yi}, where yi is the measured light output. The calibration data together with the response yf of a new dosimeter form the data D on which inference about the unknown dose df corresponding to yf is based. The general form of the calibrative density for a controlled calibration experiment is: where all densities are labeled by their arguments, stands for the model parameters and p(df) is the prior density for the unknown dose which contains ancillary information about df. The integral represents the predictive density based on the posterior density p(|Dc). We present plots of calibrative densities for both calibration data sets and different yf s. Brief remarks about calibration for integer response variables Y conclude the paper.