Description: Premium computation in a Bayesian context requires the use of a prior distribution [structure function] that the risk parameter follows in the heterogeneous portfolio. This paper contributes to the analysis of credibility theory by identifying the unique relationship between the prior distribution and credibility formula. The latter corresponds to a suggestive form of expressing the premium to be charged to a policyholder as a weighted sum of the sample mean and collective premium. Results for net premium principle and Poisson and negative binomial likelihood functions are shown.