  Experience rating in insurance uses a Bayesian credibility model to upgrade
the current premiums of a contract by taking into account policyholders'
attributes and their claim history. Most data-driven models used for this task
are mathematically intractable, and premiums must be obtained through numerical
methods such as simulation via MCMC. However, these methods can be
computationally expensive and even prohibitive for large portfolios when
applied at the policyholder level. Additionally, these computations become
``black-box" procedures as there is no analytical expression showing how the
claim history of policyholders is used to upgrade their premiums. To address
these challenges, this paper proposes a surrogate modeling approach to
inexpensively derive an analytical expression for computing the Bayesian
premiums for any given model, approximately. As a part of the methodology, the
paper introduces a \emph{likelihood-based summary statistic} of the
policyholder's claim history that serves as the main input of the surrogate
model and that is sufficient for certain families of distribution, including
the exponential dispersion family. As a result, the computational burden of
experience rating for large portfolios is reduced through the direct evaluation
of such analytical expression, which can provide a transparent and
interpretable way of computing Bayesian premiums.
