The process of associating spectral peaks in emission radiation data with particular charge states of specific elements is a common task in the field of plasma diagnostics in both laboratory and astrophysical settings. Existing techniques for this purpose are often highly manual or can rely heavily on theoretical models and assumptions of plasma parameters. We present a numerical approach to largely automate this process. The approach combines statistics from experimental data with theoretical predictions of transition strengths and observed emission intensity data in order to accomplish the task of spectral line identification in a rigorous, quantitative way, reporting confidence levels in its own predictions for each wavelength. Weighted by this confidence, the method identifies sources of 31 test emission lines in the C-2W device with 99.99% accuracy (compared to manual identification). Similar performance is demonstrated on synthetic datasets and spectroscopic observations of the planetary nebula NGC 6543, with accuracies of between 95% and 100%. The approach is scalable, portable to a wide variety of spectroscopic datasets and significantly faster and more rigorous than manual methods.