They deal with parameter inference, model comparison, and model averaging applications to gain information on the magnetic field and the plasma conditions in structures in the solar corona and in solar prominences. In the last decade, about 25 studies in coronal seismology have made use of Bayesian techniques. The first study that made use of Bayesian analysis in coronal seismology was by Arregui and Asensio Ramos (2011), who inferred coronal loop physical parameters from observed periods and damping times of their transverse oscillations. Initial solar applications were focused on statistical analyses of solar neutrino data ( Gates et al., 1995), followed by studies on solar flare prediction ( Wheatland, 2004), the analysis of solar global oscillations ( Marsh et al., 2008), and the inversion of magnetic and thermodynamic properties of the solar atmosphere from the analysis of spectro-polarimetric data ( Asensio Ramos et al., 2007). It took two more decades for the Bayesian approach to be adopted in solar physics. The first studies (already 50 years ago) dealt with both technical problems, such as the construction of image restoration algorithms ( Richardson, 1972), as well as with procedures for formalising the evaluation of astrophysical hypotheses by comparison between theoretical predictions and observational data ( Sturrock, 1973). Figure 1 shows the number of Bayesian astrophysics papers as a function of year. Since the values of the density and density contrast have probabilistic distributions, the derived magnetic field has a probabilistic distribution.īayesian analysis is increasingly being used in astrophysics. Only after assumptions about the loop plasma density and the density contrast one can derive the magnetic field.
A prototypical example is the determination of the magnetic field strength in coronal loops from the observational measurement of the kink speed of transverse oscillations ( Nakariakov and Ofman, 2001). As a consequence, solar atmospheric seismology deals with inversion problems that are probabilistic in nature and our conclusions can only be probabilities at best. Because of our lack of direct access to the physical systems of interest information is incomplete and uncertain. Coronal seismology aims to infer difficult to measure physical parameters in magnetic and plasma structures, such as coronal loops and prominence plasmas, by a combination of observations of wave activity and theoretical models, usually under the MHD approximation ( Uchida, 1970 Roberts et al., 1984). The aim of this paper is to give a rationale for the use of Bayesian methods in the study of the solar corona and to show recent applications in the area of solar coronal seismology.
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