Details Concerning Conservative, Approximate Confidence Intervals for Paired Counting of the Form [0, xx.xx]
W. E. Potter
In the past, both exact computer codes and a conservative, approximate equation for Neyman-Pearson confidence intervals, for paired counting, of the form [0, xx.xx] have been discussed. The purpose of this article is to clarify past discussions about the conservative approximation. Confidence intervals provide a way to interpret low-level measurements in radioactivity that may arise in material detection issues. Confidence intervals assist in interpreting negative net counts. Extensive numerical experimentation yields the following conservative property of the approximate value for xx.xx: the approximate value for xx.xx is equal to or greater than the exact value when the confidence level is 90, 95, 97.5, 99, and 99.9%. For the approximate value for xx.xx to be conservative the confidence coefficients used in the equation for xx.xx are taken to be 1.282, 1.645, 1.97, 2.33, and 3.11, respectively. In the above it is assumed that a good estimate is available for the expected blank count, B, and that B is stated to no more than two digits of precision in the range [0.100 to 100] and no more than one digit of precision in the range [0.00012, 0.10]. Using the fact that for the confidence levels discussed in this paper nonzero values of xx.xx increase as B increases, values of B are rounded up to either two or one digit of precision. Also, the observed net count, OC, is taken to be equal to or less than 100 and a stopping rule is necessary for OC less than 1 and confidence levels of 97.5, 99, and 99.9%. The stopping rule is utilized only if xx.xx is calculated to be 0.0 for either OC or (OC 1), in which case xx.xx is assigned the value calculated for (OC + 1). Conservative confidence intervals for the expected value of the Poisson distribution follow from the same equation upon setting B = 0.0.
This abstract was presented at the 38th Annual Midyear Meeting, "Materials Control and Security: Risk Assessment, Handling, and Detection", Advances in Instrumentation, Materials Detection and Measurement Session, 2/13/2005 - 2/16/2005, held in New Orleans, LA.