Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Models

TL;DR

This paper introduces a flexible simulation-based method for translating diverse forms of expert knowledge into prior distributions for Bayesian models, applicable across various model types and elicitation techniques.

Contribution

It develops a novel, model-agnostic elicitation approach that learns prior hyperparameters from different expert knowledge formats using stochastic gradient descent.

Findings

Effective across linear, generalized linear, and hierarchical models

Robust to different expert knowledge formats

Independent of underlying model structure

Abstract

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.