# Application of the Approximate Bayesian Computation Algorithm to Gamma-Ray Spectroscopy
## 1 Introduction  
The energy spectra of gamma-rays emitted by radioisotopes act as fingerprints that enable the identification of the source. Such identification over short time periods is challenging for several reasons, including Poisson fluctuations in counts, relatively large isotope libraries with some peak overlaps, environmental effects, shielding effects such as missing peaks, single-escape and double-escape peaks due to electron pair production, pulse pileup and deadtime effects at relatively high count rates, as well as energy-dependent and sample-dependent detector efficiencies [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21].  
The term \"unfolding\" in gamma spectroscopy refers to several steps used to infer the features of the source that generated the spectrum [10]. The main gamma spectrum unfolding tasks are spectral data smoothing (as a form of noise reduction), background subtraction, peak searching (overlapping peak separation), peak area calculation, and radioisotope identification (RIID) [7; 11].  
There is reason to believe that RIID performance using, for example, Sodium Iodide (NaI) detectors (a very common fielded gamma ray detector) can be improved [7; 8; 9; 10; 11]. This paper will show the strong potential of approximate Bayesian computation (ABC) in peak location and area estimation, plus in simple RIID applications using either peak information or other features of the spectra collected by NaI detectors. Since [7], several RIID advances have been made. For example, [8] introduced aBayesian approach applied to extracted peak locations and area ratios; [9] used convolution neural networks applied to simulated spectra; [10] applied the least absolute shrinkage and selection operator (LASSO) that is well known to be effective for subset selection. The first goal of an RIID algorithm is to choose which subset from a library of a few 10 s to approximately 100 radioisotopes (including medical, threat, industrial, and naturally occurring radioactive materials) is likely to be contained in a test item. The second goal is to estimate the amount of each isotope thought to be present in the item. One key validation step in any modern RIID is to simulate data assuming that the item contains the chosen isotope subset using a \"forward model\" that requires an estimate of the gamma detector response function (DRF) [11; 12; 13; 18; 19; 20; 21]. If the simulated data agree reasonably well with the observed data, then there is reasonable confidence that the inferred subset is at least close to correct. However, simulation model bias is not yet considered in any existing RIID to our knowledge. The ABC algorithm [22] provides a natural option to allow for model bias and this leads to the proposed new ABC-based RIID.  
This paper is organized as follows. Section 2 provides additional background for gamma-ray spectroscopy. Section 3 briefly describes existing peak location algorithms. Section 4 briefly describes smoothing algorithms. Section 5 describes ABC and peak location and area estimation. Section 6 illustrates a newly developed ABC-based RIID.