= Bühlmann credibility for inverse-gamma observations
{c}
{title2=$Z=\frac{n(k-2)}{n(k-2)+\alpha+1}$}
In the <Gamma prior for an inverse-gamma scale> model, assume $k>2$. The <variance of hypothetical means> is $a=\alpha/[\lambda^2(k-1)^2]$, and the <expected process variance> is $v=\alpha(\alpha+1)/[\lambda^2(k-1)^2(k-2)]$. The <Bühlmann credibility factor> is $Z=n/(n+v/a)$, giving the displayed expression. The optimal affine <credibility estimate> is $(1-Z)\alpha/[\lambda(k-1)]+Z\overline X$. Its fixed-weight arithmetic-mean form differs from the reciprocal-based <posterior mean>.
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