= Evidence averaging under an interval prior
{title2=$Z=(b-a)^{-1}\int_a^b\mathcal L(\theta)\,d\theta$}
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.
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