Bayesian parameter inference with stochastic solar dynamo models

Abstract

Time-series of cosmogenic radionuclides stored in natural archives such as ice cores and tree rings are a proxy for solar magnetic activity on multi-millennial time-scales. Radionuclides data exhibit a number of interesting features such as intermittent stable cycles of high periods and Grand Minima. Although a lot of effort has gone into the development of sound physically based stochastic solar dynamo models, it is still largely unclear what are the underlying mechanisms that lead to the observed phenomena. Answering these questions requires quantitatively calibrating the models to the data and comparing performances of different models with the associated uncertainties in model parameters and predictions. Bayesian statistics is a consistent framework for parameter inference where knowledge about model parameters is expressed through probability distributions and updated using measured data. However, Bayesian inference with non-linear stochastic models can become computationally extremely expensive and it is therefore hardly ever applied. In recent years, sophisticated and scalable algorithms have emerged, which have the potential of making Bayesian inference for complex stochastic models feasible. We intend to investigate the power of Approximate Bayesian Computation (ABC) and Hamiltonian Monte Carlo (HMC) algorithms. We present our first inference results with stochastic solar dynamo models