 Evidence averaging under an interval prior

For a normalized uniform prior on $[a,b]$, Bayesian model evidence is $Z=(b-a{)}^{-1}{\int }_a^b\mathcal{L}(\theta )d\theta$. It averages the likelihood over the prior range. Extending a well-placed interval into low-likelihood regions reduces that average, but moving or widening a poorly placed interval can improve it. A model prior is separate: posterior model odds equal the evidence ratio multiplied by prior model odds.