A Bayesian approach to comparing theoretic models to observational data: A case study from solar flare physics

Abstract

Solar flares are large-scale releases of energy in the solar atmosphere, which are characterized by rapid changes in the hydrodynamic properties of plasma from the photosphere to the corona. Solar physicists have typically attempted to understand these complex events using a combination of theoretical models and observational data. From a statistical perspective, there are many challenges associated with making accurate and statistically significant comparisons between theory and observations, due primarily to the large number of free parameters associated with physical models. This class of ill-posed statistical problem is ideally suited to Baysian methods. In this paper, the solar flare studied by Raftery et al. (2008) is reanalysed using a Baysian framework. This enables us to study the evolution of the flare's temperature, emission measure and energy loss in a statistically self-consistent manner. The Baysian-based techniques confirm that both conductive and non-thermal beam heating play important roles in heating the flare plasma during the impulsive phase of this event.