= Bernoulli saturated log-likelihood
{c}
{title2=$\ell_{\mathrm{sat}}=0$}
For individual <Bernoulli> observations, the <statistical saturated model> assigns one independent probability to each response. Each <likelihood> factor is at most one and is exactly one at $\pi_i=y_i$. Hence the maximum <log-likelihood> is zero, with $0\log0=0$. This boundary maximum is attained when probabilities zero and one are allowed; restricting them to the open interval gives the same supremum.
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