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A method is presented for Bayesian model selection without explicitlycomputing evidences, by using a combined likelihood and introducing an integermodel selection parameter $n$ so that Bayes factors, or more generallyposterior odds ratios, may be read off directly from the posterior of $n$. Ifthe total number of models under consideration is specified a priori, the fulljoint parameter space $(\theta, n)$ of the models is of fixed dimensionalityand can be explored using standard Markov chain Monte Carlo (MCMC) or nestedsampling methods, without the need for reversible jump MCMC techniques. Theposterior on $n$ is then obtained by straightforward marginalisation. Wedemonstrate the efficacy of our approach by application to several toy models.We then apply it to constraining the dark energy equation-of-state using afree-form reconstruction technique. We show that $\Lambda$CDM is significantlyfavoured over all extensions, including the simple $w(z){=}{\rm constant}$model.

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