Simulated Annealing and Bayesian Posterior Distribution Analysis Applied to Spectral Emission Line Fitting

Spectral-line fitting problems are extremely common in all remote-sensing disciplines, solar physics included. Spectra in solar physics are frequently parameterized by using a model for the background and the emission lines, and various computational techniques are used to find values to the parameters given the data. However, the most commonly-used techniques, such as least-squares fitting, are highly dependent on the initial parameter values used and are therefore biased. In addition, these routines occasionally fail because of ill-conditioning. Simulated annealing and Bayesian posterior distribution analysis offer different approaches to finding parameter values through a directed, but random, search of the parameter space. The algorithms proposed here easily incorporate any other available information about the emission spectrum, which is shown to improve the fit. Example algorithms are given and their performance is compared to a least-squares algorithm for test data – a single emission line, a blended line, and very low signal-to-noise-ratio data. It is found that the algorithms proposed here perform at least as well or better than standard fitting practices, particularly in the case of very low signal-to-noise ratio data. A hybrid simulated annealing and Bayesian posterior algorithm is used to analyze a Mg x line contaminated by an O IV triplet, as observed by the Coronal Diagnostic Spectrometer onboard SOHO. The benefits of these algorithms are also discussed.