Bayesian model selection without evidences: application to the dark energy equation-of-state

Understand

A method is presented for Bayesian model selection without explicitly computing evidences, by using a combined likelihood and introducing an integer model selection parameter $n$ so that Bayes factors, or more generally posterior odds ratios, may be read off directly from the posterior of $n$.

• If the total number of models under consideration is specified a priori, the full joint parameter space $(\theta, n)$ of the models is of fixed dimensionality and can be explored using standard Markov chain Monte Carlo (MCMC) or nested sampling methods, without the need for reversible jump MCMC techniques.
• The posterior on $n$ is then obtained by straightforward marginalisation.
• We demonstrate the efficacy of our approach by application to several toy models.