= Bühlmann model
{c}
{title2=$m=\mathbb E[m(\Theta)],\ v=\mathbb E[v(\Theta)],\ a=\operatorname{Var}(m(\Theta))$}
Given a latent risk parameter $\Theta$, observations are <independent and identically distributed random variables> with <conditional expectation> $m(\Theta)$ and <conditional variance> $v(\Theta)$. The <Bühlmann credibility premium> estimates $m(\Theta)$ by an affine function of past observations under <mean squared error>. Its population parameters are $m=\mathbb Em(\Theta)$, <expected process variance> $v=\mathbb Ev(\Theta)$, and <variance of hypothetical means> $a=\operatorname{Var}(m(\Theta))$.
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