Model selection for spectro-polarimetric inversions

TL;DR

This paper introduces a quantitative Bayesian evidence-based method for selecting the most appropriate atmospheric models in spectropolarimetric inversions, improving objectivity and consistency in solar magnetic field analysis.

Contribution

It presents the first use of Bayesian evidence ratios for model comparison in spectropolarimetric inversions, providing an objective criterion for model complexity.

Findings

Moderate SNR data favor simpler models without gradients.

High SNR data favor more complex models with gradients.

Evidence ratios correlate with simple proxies, enabling easier model comparison.

Abstract

Inferring magnetic and thermodynamic information from spectropolarimetric observations relies on the assumption of a parameterized model atmosphere whose parameters are tuned by comparison with observations. Often, the choice of the underlying atmospheric model is based on subjective reasons. In other cases, complex models are chosen based on objective reasons (for instance, the necessity to explain asymmetries in the Stokes profiles) but it is not clear what degree of complexity is needed. The lack of an objective way of comparing models has, sometimes, led to opposing views of the solar magnetism because the inferred physical scenarios are essentially different. We present the first quantitative model comparison based on the computation of the Bayesian evidence ratios for spectropolarimetric observations. Our results show that there is not a single model appropriate for all profiles simultaneously. Data with moderate signal-to-noise ratios favor models without gradients along the line-of-sight. If the observations shows clear circular and linear polarization signals above the noise level, models with gradients along the line are preferred. As a general rule, observations with large signal-to-noise ratios favor more complex models. We demonstrate that the evidence ratios correlate well with simple proxies. Therefore, we propose to calculate these proxies when carrying out standard least-squares inversions to allow for model comparison in the future.