Efficient Inference of Solar Rotation Profiles: An Analysis of Markov Chain Monte Carlo and Hamiltonian Monte Carlo

Abstract

Standard attempts to infer solar flow profiles have largely depended on frequency-splitting measurements via a-coefficients. The isolated multiplet approximation that these techniques are based on fails to hold for non-axisymmetric flows and high angular degrees. Analysis of eigenfunction corrections, which account for mode coupling provides a more flexible approach, but standard inference techniques yield large spread and potential random-walk inefficiencies. We demonstrate that an HMC approach to inference exhibits quick convergence, strong consistency, and thorough exploration of parameter space, but fails to deal with diverging orders of magnitude. With further modification, the results provide a promising new avenue for a-coefficient inference.