Constraining coronal heating: employing Bayesian analysis techniques to improve the determination of solar atmospheric plasma parameters

TL;DR

This paper introduces Bayesian analysis techniques to improve the comparison of coronal heating models with observational data, providing a more robust statistical framework than traditional methods.

Contribution

It presents an alternative Bayesian approach for model comparison in coronal heating studies, validated with simulated data and applied to real datasets.

Findings

Bayesian methods can better distinguish heating mechanisms under certain error conditions.

Traditional $hi^2$ approach has limitations in coronal plasma parameter analysis.

Bayesian analysis offers a more flexible framework for model selection in solar physics.

Abstract

One way of revealing the nature of the coronal heating mechanism is by comparing simple theoretical one dimensional hydrostatic loop models with observations at the temperature and/or density structure along these features. The most well-known method for dealing with comparisons like that is the $\chi^2$ approach. In this paper we consider the restrictions imposed by this approach and present an alternative way for making model comparisons using Bayesian statistics. In order to quantify our beliefs we use Bayes factors and information criteria such as AIC and BIC. Three simulated datasets are analyzed in order to validate the procedure and assess the effects of varying error bar size. Another two datasets (Ugarte-Urra et al., 2005; Priest et al., 2000) are re-analyzed using the method described above. In one of these two datasets (Ugarte-Urra et al., 2005), due to the error estimates in the observed temperature values, it is not posible to distinguish between the different heating mechanisms. For this we suggest that both Classical and Bayesian statistics should be applied in order to make safe assumptions about the nature of the coronal heating mechanisms.