MEASUREMENT OF AIRBORNE RADON DAUGHTERS - A BAYESIAN-APPROACH

The standard mathematical treatment of the build-up and decay of airbo rne radionuclides on a filter paper uses the solutions of the so-calle d Bateman equations adapted to the sampling process. These equations c an be interpreted as differential equations for the expectation of an underlying stochastic process, which describes the random fluctuations in the accumulation and decay of the sampled radioactive atoms. The p robability distribution for the number of Po-218, Pb-214 and Bi-214 at oms, accumulated after sampling time t, is the product of three Poisso n distributions. It is shown that the distribution of the number of co unts, registered by a detector with efficiency epsilon during a counti ng period T after the end of sampling, is also the product of three Po isson distributions. Its mean is dependent on epsilon, t, T, how rate, and N-A(0), N-B(0) and N-C(0) the number of Po-218, Pb-214 and (214)G i atoms per unit volume. This joint Poisson distribution was used to c onstruct the likelihood given the observed number of counts. Using Bay es' Theorem posterior densities were obtained for N-A(0), N-B(0) and N -C(0). These densities characterise the remaining uncertainty about th e unknown airborne concentrations of Po-218, Pb-214 and Bi-214 atoms.