Measurement of airborne {sup 218}Po - A Bayesian approach
- Univ. of Tennessee, Knoxville, TN (United States)
The standard mathematical treatment of the buildup and decay of airborne radionuclides on a filter paper uses the solutions of the so-called bateman equations adapted to the sampling process. The equations can 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 process for the buildup and decay of airborne {sup 218}Po can be characterized as an {open_quotes}immigration-death process{close_quotes} in the widely adopted, biologically based jargon. The probability distribution for the number of {sup 218}Po atoms, accumulated after sampling time t, is Poisson. We show that the distribution of the number of counts, registered by a detector with efficiency {epsilon} during a counting period T after the end of sampling, it also Poisson, with mean dependent on {epsilon},t,T, the flowrate and N{sub o}, the number of airborne {sup 218}Po atoms per unit volume. This Poisson distribution was used to construct the likelihood given the observed number of counts. After inversion with Bayes` Theorem we obtained the posterior density for N{sub o}. This density characterizes the remaining uncertainty about the measured under of {sup 218}Po atoms per unit volume of air. 6 refs., 3 figs., 1 tab.
- OSTI ID:
- 420447
- Journal Information:
- Health Physics, Vol. 71, Issue 6; Other Information: PBD: Dec 1996
- Country of Publication:
- United States
- Language:
- English
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