= Gaussian temporal-discrepancy shrinkage
{title2=$E[\delta\mid y]=y\tau^2/(s^2+\tau^2)$}
For a common-event model, let $y\mid\delta\sim N(\delta,s^2)$ and $\delta\sim N(0,\tau^2)$ with positive <variances>. The posterior exponent is $-[(y-\delta)^2/s^2+\delta^2/\tau^2]/2$. Completing the square yields posterior precision $s^{-2}+\tau^{-2}$ and mean $y\tau^2/(s^2+\tau^2)$. The estimate is pulled toward zero, more strongly when the measurement is uncertain. This conditional model does not decide whether a common event should be assumed.
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