Markov Walk Exploration of Model Spaces: Bayesian Selection of Dark Energy Models with Supernovae

Abstract: Central to model selection is a trade-off between performing a good fit and low model complexity: A model of higher complexity should only be favoured over a simpler model if it provides significantly better fits. In Bayesian terms, this can be achieved by considering the evidence ratio, enabling choices between two competing models. We generalise this concept by constructing Markovian random walks for exploring the entire model space. In analogy to the logarithmic likelihood ratio in parameter estimation problem, the process is governed by the logarithmic evidence ratio. We apply our methodology to selecting a polynomial for the dark energy equation of state function $w(a)$ on the basis of data for the supernova distance-redshift relation.