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

TL;DR

This paper introduces a Bayesian Markov walk method for exploring model spaces, applied to selecting dark energy models based on supernova data, balancing fit quality and complexity.

Contribution

It generalizes Bayesian model selection by constructing Markovian random walks guided by evidence ratios, enabling comprehensive exploration of model spaces.

Findings

Effective exploration of model space demonstrated

Successful application to dark energy polynomial selection

Provides a new framework for Bayesian model comparison

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.