Laplace-likelihood interval evidence
= Laplace-likelihood interval evidence
{c}
{title2=$Z/C=(s/w)(1-e^{-w/s})$}
If $\mathcal L(\theta)=C e^{-|\theta-\mu|/s}$, integrate the two exponential branches at $\mu$. An interval of half-width $w$ centred at $\mu$ has $Z/C=(s/w)(1-e^{-w/s})$. An interval entirely below the peak has $Z/C=s[e^{(b-\mu)/s}-e^{(a-\mu)/s}]/(b-a)$. These expressions show quantitatively how fit location and prior width combine.