## 3 Problem Statement  
The most general challenging problem in our context of screening for threat isotopes requires an isotope library of approximately 200 radio-isotopes and contains several unknown factors, including an unknown source (single or multiple isotopes) in unknown form (gas, liquid, solid) in unknown geometry with unknown shielding, unknown distance between the source and detector, and unknown potential for electronics drifting. Most RIID algorithms insist that the detector properties are known as specified by standard vendor specifications, and so the detector's energy resolution, efficiency at a given distance from the source, and calibration are at least fairly well known. The main inference goal is to identify all isotopes present in the source, and also quantify the isotopes. Absorbing materials between the source and detector and in the detector distort peak shapes and overall spectral shape which complicates the main inference task. Typically, inferring the type and amount of shielding is not a primary goal but instead is a secondary goal because an estimate of shielding material can improve source identification. Many screening locations apply RIID algorithms using hand-held NaI detectors scanning only those cases (vehicles, people, cargo, containers, etc., depending on specific application) that were found in initial gross-count screening to have significantly higher-than-background radiation [8]. The measurement protocol for such hand-held detectors can vary depending on operations at each deployment. Therefore, special cases of the general problem are of interest in which some of these factors are known. For example, the source might be known to be a solid in a vehicle at a known distance from a hand-held NaI detector. Also, in some applications, the inference goal is to infer whether the source isotopes belong to medical, industrial, NORM, or SNM categories. Medical isotopes include \({}^{67}\)Ga, \({}^{51}\)Cr, \({}^{75}\)Se, \({}^{99m}\)Tc, \({}^{103}\)Pd, \({}^{111}\)In, \({}^{123}\)I, \({}^{125}\)I, \({}^{131}\)I, \({}^{201}\)Tl, and \({}^{133}\)Xe. Industrial isotopes include \({}^{57}\)Co, \({}^{60}\)Co, \({}^{133}\)Ba, \({}^{137}\)Cs, \({}^{192}\)Ir, \({}^{204}\)Tl, \({}^{226}\)Ra, and \({}^{241}\)Am. NORM isotopes include \({}^{40}\)K, \({}^{226}\)Ra, \({}^{232}\)Th and its daughters, and \({}^{238}\)U and its daughters. SNM isotopes include \({}^{233}\)U, \({}^{235}\)U, \({}^{237}\)Np, and Pu isotopes. Whenever any of the factors such as source-to-detector distance, shielding materials, number of source isotopes, identity of possible source isotopes, or degree of electronic stability, is known, one can tailor the RIID algorithm accordingly for improved results. For example [9], requires an instrument vendor's RIID algorithm to specify what isotopes it can identify and their category. Reference [9] also requires the RIID algorithm to recognize each isotope in a specific list of approximately 20 isotopes including some of those listed above. Note that if a RIID algorithm must only recognize 20 isotopes, then custom isotope libraries could be extracted from the more complete library of approximately 200 isotopes. As a qualitative example of how distinguishable various isotopes are, Figure 2 plots two example scaled NaI detector spectra from each of \({}^{239}\)Pu, \({}^{235}\)U, and \({}^{137}\)Cs. A small \({}^{137}\)Cs check source is present in this detector, so the \({}^{239}\)Pu and \({}^{235}\)U spectra have peaks near 662 keV associated with a 662 keV \(\gamma\) emitted from \({}^{137}\)Cs. The same scaling as in Figure 1 was used. **Figure 2.** Two example scaled spectra from each of \({}^{239}\)Pu, \({}^{235}\)U, and \({}^{137}\)Cs. A small \({}^{137}\)Cs check source is present in this detector, so the \({}^{239}\)Pu and \({}^{235}\)U spectra have peaks near 662 keV associated with a 662 keV \(\gamma\) emitted from \({}^{137}\)Cs. **4.