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We review the effect that the choice of a uniform or logarithmic prior has onthe Bayesian evidence and hence on Bayesian model comparisons when data provideonly a one-sided bound on a parameter. We investigate two particular examples:the tensor-to-scalar ratio $r$ of primordial perturbations and the mass ofindividual neutrinos $m_\nu$, using the cosmic microwave background temperatureand polarisation data from Planck 2018 and the NuFIT 5.0 data from neutrinooscillation experiments. We argue that the Kullback-Leibler divergence, alsocalled the relative entropy, mathematically quantifies the Occam penalty. Wefurther show how the Bayesian evidence stays invariant upon changing the lowerprior bound of an upper constrained parameter. While a uniform prior on thetensor-to-scalar ratio disfavours the $r$-extension compared to the base LCDMmodel with odds of about 1:20, switching to a logarithmic prior renders bothmodels essentially equally likely. LCDM with a single massive neutrino isfavoured over an extension with variable neutrino masses with odds of 20:1 incase of a uniform prior on the lightest neutrino mass, which decreases toroughly 2:1 for a logarithmic prior. For both prior options we get only a veryslight preference for the normal over the inverted neutrino hierarchy withBayesian odds of about 3:2 at most.

Bayesian evidence for the tensor-to-scalar ratio $r$ and neutrino masses $m_\nu$: Effects of uniform vs logarithmic priors