Two New Approaches to Determining Parameter Values to Emission Spectra From RHESSI

We examine two new approaches to determining parameter values to emission spectra from RHESSI. Simulated annealing removes much of the bias inherent in initializing commonly used deterministic routines through implementing a parameter space search minimizing a suitable cost function (such as sum of squares of differences between data and a parameterized curve). This search gradually moves from being a full random search to a directed search where only parameter values which minimize the cost function are accepted. In comparison, Markov Chain Monte Carlo methods are used to sample from the Bayesian posterior distribution constructed from prior information on the observation (such as the number of emission lines present and likely parameter values) as well as the data itself. Parameter values can then be assigned by constructing the appropriate averages from the data. These methods have the advantage of sidestepping many of the problems of traditional analysis routines (for example, ill-conditioned matrices) whilst allowing the easy inclusion of other information, such as parameter constraints. Both approaches are applied to RHESSI spectroscopic data, and are compared to more commonly used routines. RHESSI is comprised of separate detectors which allows us to conduct 9 independent measurements of the same solar flux over any time interval. Since these new methods return important information about the dispersion in a parameter from counting statistics, then the multi-detector sample will also contain important insight into the sources of systematic deviations.