= Threshold-censored normal likelihood
{title2=$L(\mu,\sigma)=\prod_i\Phi(s_i(\mu-c_i)/\sigma)$}
Suppose conditionally independent latent values have <normal distribution> $N(\mu,\sigma^2)$, with $\sigma>0$, but the observation only says which side of a known threshold $c_i$ contains each value. With $s_i=1$ for a value above the threshold and $s_i=-1$ for a value below, the <likelihood> is the displayed product, where $\Phi$ is the <standard normal distribution function>. Repeated thresholds give corresponding powers. These factors are tail <probabilities>, not <probability densities> evaluated at the thresholds. Multiplying normal densities at $c_i$ would describe a different observation process. The thresholds must be treated as fixed or otherwise modelled appropriately; informative selection of thresholds can change the <likelihood>.
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