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Developing Detection DecisioNS on the Absence or Presence of a Radiological Source using a Bayesian Interaction Model

Brogan, John; Brandl, Alexander1

doi: 10.1097/HP.0000000000001104

Bayesian statistics have been used in various health physics applications, but only limited material exists on the development of a decision threshold for simple gross count measurements using Bayesian statistics. Bayesian modeling specifies a logical procedure for processing information and provides the means to obtain abstract statistical knowledge about the data in question. A Bayesian interaction model was developed to analyze gross count measurements. This linear regression model studies the relationship between a gross count measurement and the standard deviation of the gross counts obtained in the current and the previous four measurements, and conditions the analysis on whether the data originate from background measurements or from measurements with a source present. The measure of that relationship is expressed statistically by the constructed parameter ζ, which in the Bayesian framework possesses a probability distribution that can be used to achieve detection decisions. The model was validated statistically and under operationally equivalent conditions. Specifically, it was applied to analyze sequential data obtained from continuous gross count measurements at fixed time intervals. The Bayesian analysis used five sequential measurements per detection decision. The model performs optimally for weaker source detections, and presents promising operational application. Its usefulness derives from the facts that an established training data set is not necessary, long-run background measurements are not required to establish parameter estimates, and ζ and the model are universally applicable such that their use is not limited to the predictor variable presented here.

1Colorado State University, Fort Collins, CO.

The authors declare no conflicts of interest.

For correspondence contact Alexander Brandl, Colorado State University, 1618 Campus Delivery, Fort Collins, CO 80523, or email at

(Manuscript accepted 17 March 2019)

Online date: May 24, 2019

© 2019 by the Health Physics Society