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 characterised 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 Bayesian methods. In this paper, the solar flare studied by Raftery et al. ( 2009) is reanalysed using a Bayesian 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 Bayesian-based model selection techniques imply that no decision can be made regarding which of the conductive or non-thermal beam heating play the most important role in heating the flare plasma during the impulsive phase of this event.