  A central characteristic of Bayesian statistics is the ability to
consistently incorporate prior knowledge into various modeling processes. In
this paper, we focus on translating domain expert knowledge into corresponding
prior distributions over model parameters, a process known as prior
elicitation. Expert knowledge can manifest itself in diverse formats, including
information about raw data, summary statistics, or model parameters. A major
challenge for existing elicitation methods is how to effectively utilize all of
these different formats in order to formulate prior distributions that align
with the expert's expectations, regardless of the model structure. To address
these challenges, we develop a simulation-based elicitation method that can
learn the hyperparameters of potentially any parametric prior distribution from
a wide spectrum of expert knowledge using stochastic gradient descent. We
validate the effectiveness and robustness of our elicitation method in four
representative case studies covering linear models, generalized linear models,
and hierarchical models. Our results support the claim that our method is
largely independent of the underlying model structure and adaptable to various
elicitation techniques, including quantile-based, moment-based, and
histogram-based methods.
