  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 spaces governed by the
logarithmic evidence ratio, in analogy to the logarithmic likelihood ratio in
parameter estimation problems. The theory of Markovian model exploration has an
analytical description with partition functions, which we derive for both the
canonical and macrocanonical case. We apply our methodology to selecting a
polynomial for the dark energy equation of state function $w(a)$ fulfilling
sensible physical priors, on the basis of data for the supernova
distance-redshift relation. We conclude by commenting on Jeffreys' scale for
Bayesian evidence ratios, choices of model priors and derived quantities like
Shannon entropies for posterior model probabilities.
