Sequential Bühlmann credibility update
= Sequential Bühlmann credibility update
{title2=$\widehat m_{n+1}=\widehat m_n+(x_{n+1}-\widehat m_n)/(n+1+K)$}
With fixed structural parameters and $K=v/a$, the <Bühlmann credibility estimate> has form $(\sum_{i=1}^nx_i+Km_0)/(n+K)$. The next observation updates it by the displayed rule. Consequently the estimate decreases exactly when the new observation is less than the previous credibility estimate, with strict equality handled separately.