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We present the application of the Markov Chain Monte Carlo (MCMC) and Bayesian inference methods to the seismological measurements of the coronal loop parameters from the decaying kink oscillations. Such estimation requires to solve the inversion problem and to find a model parameter set that is the most consistent with the observational data. We solved this problem using the Bayesian approach in combination with the Markov Chain Monte Carlo (MCMC) method. It provides a solution for accurate and robust inference of the model parameters and corresponding uncertainties.
We analysed the damping profile of decaying kink oscillations, and performed a seismological inversion of the density contrast (1.5 – 3.0) and the inhomogeneity layer width (0.5 – 1.2) for a number of coronal loops. We also compared different models by calculation of the Bayes factor and found that accounting for the additional parallel harmonics is preferable in all analysed events. We also considered a possible modification of the period ratio of the parallel harmonics, caused by the density stratification or loop expansion, and found a strong evidence for the dispersionless model in all loops but one, where the stratified model is more evident.
Thus, MCMC based Bayesian inference is a powerful and robust method and allows for accurate seismology of coronal loops, in particular the transverse density profile, and potentially reveals additional physical effects