Bayesian model selection without evidences: application to the dark
  energy equation-of-state
  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.
We then apply it to constraining the dark energy equation-of-state using a
free-form reconstruction technique. We show that $\Lambda$CDM is significantly
favoured over all extensions, including the simple $w(z){=}{\rm constant}$
model.
