Solution
= Solution
For a shape-rate <gamma distribution> $\operatorname{Gamma}(a,b)$, the mean and <variance> conditions require
$$
\frac ab=1,\qquad \frac a{b^2}=0.25^2=\frac1{16}.
$$
The first equation gives $a=b$, and the second then gives $a=b=16$. Hence
$$
\boxed{\lambda_i\sim\operatorname{Gamma}(16,16).}
$$
This proper <prior distribution> is centered on the national reference risk, while allowing genuine between-area variation.