III. IMPORTANCE OF THRESHOLD IN ML ANALYSIS OF NEUTRON WIDTHS 5 Typically, these difficulties have been surmounted by using a energy-independent thresh- old as an integral part of the ML analysis, implicitly assuming that all s -wave resonances above threshold have been observed. We recently have shown [23] that an energy-dependent threshold (on g Γ 0 $_{n}$) of the form T = a E$_{n}$ , where a is a constant factor, offers three ad- Below I will show that the NDE is seriously contaminated by p -wave resonances. It is also almost certainly incomplete, as illustrated in Figs. 1 and 2. Reduced neutron widths for all 1245 resonances in the NDE are shown as a function of resonance energy in Fig. 1, from which it can be seen that their are fewer small widths as the energy increases. This is just what is expected from well-known [22] instrumental effects that decrease sensitivity as the energy increases; hence, more small resonances are missed at higher energies. This is further illustrated in Fig. 2 in which distributions of reduced neutron widths are shown for the 100 lowest- and highest-energy NDE resonances. As can be seen in this figure, the distribution of the highest-energy set is substantially narrower (and hence is in better agreement with a χ 2 distribution having a larger ν ) than the lowest energy one. Again, this is just what is expected if more resonances are missed as energy increases. Because the PTD is a special case (degrees-of-freedom ν = 1) of the family of χ 2 dis- tributions, it is assumed that the data are distributed accordingly and the ML method is used to estimate the most likely value of ν . Ideally, the data should be complete (no missing resonances) and pure (all resonances have the same parity). Unfortunately, all experiments from which neutron widths have been determined have finite thresholds for detecting reso- nances and for separating small s - from large p -wave resonances. Not properly accounting for these effects can result in substantial systematic errors in ML estimates of ν . Given the shape of the χ 2 distribution as a function of ν , neglecting the effect of missed s -wave resonances below threshold will, in general, lead to a falsely large value of ν from the ML analysis. Conversely, including even just a few p -wave resonances in an s -wave set will, in general, lead to a falsely small value of ν . This potential problem is especially important for many of the NDE nuclides because they are near the peaks of the p - and minimum of the s -wave neutron strength functions, and therefore neutron width is a much less reliable indicator of resonance parity.