Statistical analysis of uncertainties of gamma-peak identification and area calculation in particulate air-filter environment radionuclide measurements using the results of a Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) organized intercomparison, Part I: assessment of reliability and uncertainties of isotope detection and energy precision using artificial spiked test spectra, Part II: assessment of the true type I error rate and the quality of peak area estimators in relation to type II errors using large numbers of natural spectra

Application of the Approximate Bayesian Computation Algorithm to Gamma-Ray Spectroscopy

Radioisotope identification (RIID) algorithms for gamma-ray spectroscopy aim to infer what isotopes are present and in what amounts in test items. RIID algorithms either use all energy channels in the analysis region or only energy channels in and near identified peaks. Because many RIID algorithms rely on locating peaks and estimating each peak’s net area, peak location and peak area estimation algorithms continue to be developed for gamma-ray spectroscopy. This paper shows that approximate Bayesian computation (ABC) can be effective for peak location and area estimation. Algorithms to locate peaks can be applied to raw or smoothed data, and among several smoothing options, the iterative bias reduction algorithm (IBR) is recommended; the use of IBR with ABC is shown to potentially reduce uncertainty in peak location estimation. Extracted peak locations and areas can then be used as summary statistics in a new ABC-based RIID. ABC allows for easy experimentation with candidate summary statistics such as goodness-of-fit scores and peak areas that are extracted from relatively high dimensional gamma spectra with photopeaks (1024 or more energy channels) consisting of count rates versus energy for a large number of gamma energies.

Probability of Type-I errors in the peak analyses of gamma-ray spectra

The probability density of Type-I errors in the peak-locating step of the spectra-analyzing procedure was empirically determined at a low value of the sensitivity parameter for peak recognition as a function of the height of the continuous spectral background and peak width. On the basis of this probability density, the number of Type-I errors for any spectral shape and FWHM calibration can be estimated. A criterion that is based on the relative peak-area uncertainty and the relative difference between the peak width obtained from the FWHM calibration and the width reported by the peak-analyzing program, as a measure of the believability that a located peak presents a Type-I error, is established. In addition, we demonstrate that the peaks having the largest believability are most likely to originate from Type-I errors. Using this criterion, the number of peaks, not identified in the identification step of the spectra analyzing procedure, to be checked for their origin can be reduced in accordance with the number of estimated Type-I errors.