Large passive detectors used in screening for special nuclear materials at ports of entry are characterized by poor spectral resolution, making identification of radionuclides a difficult task. Most identification routines, which fit empirical shapes and use derivatives, are impractical in these situations. Here I develop new, physics-based methods to determine the presence of spectral signatures of one or more of a set of isotopes. Gamma-ray counts are modeled as Poisson processes, where the average part is taken to be the model and the difference between the observed gamma-ray counts and the average is considered random noise. In the linear part, the unknown coefficients represent the intensites of the isotopes. Therefore, it is of great interest not to estimate each coefficient, but rather determine if the coefficient is non-zero, corresponding to the presence of the isotope. This thesis provides new selection algorithms, and, since detector data is undoubtedly finite, this unique work emphasizes selection when data is fixed and finite.