We revisit the classical credibility results of Jewell and B\"uhlmann to
obtain credibility premiums for a GLM using a modern Bayesian approach. Here
the prior distributions can be chosen without restrictions to be conjugate to
the response distribution. It can even come from out-of-sample information if
the actuary prefers.
Then we use the relative entropy between the "true" and the estimated models
as a loss function, without restricting credibility premiums to be linear. A
numerical illustration on real data shows the feasibility of the approach, now
that computing power is cheap, and simulations software readily available
