When developing Bayesian hierarchical models, selecting the most appropriate hierarchical structure can be a challenging task, and visualisation remains an underutilised tool in this context. In this paper, we consider visualisations for the display of hierarchical models in data space and compare a collection of multiple models via their parameters and hyper-parameter estimates. Specifically, with the aim of aiding model choice, we propose new visualisations to explore how the choice of Bayesian hierarchical modelling structure impacts parameter distributions. The visualisations are designed using a robust set of principles to provide richer comparisons that extend beyond the conventional plots and numerical summaries typically used. As a case study, we investigate five Bayesian hierarchical models fit using the brms R package, a high-level interface to Stan for Bayesian modelling, to model country mathematics trends from the PISA (Programme for International Student Assessment) database. Our case study demonstrates that by adhering to these principles, researchers can create visualisations that not only help them make more informed choices between Bayesian hierarchical model structures but also enable them to effectively communicate the rationale for those choices.

翻译：在开发贝叶斯分层模型时，选择最合适的分层结构往往具有挑战性，而可视化技术在此领域的应用仍显不足。本文探讨了在数据空间中展示分层模型的可视化方法，并通过参数与超参数估计值对多个模型集合进行比较。具体而言，为辅助模型选择，我们提出了新的可视化方案，用以探索贝叶斯分层建模结构的选择如何影响参数分布。这些可视化设计基于一套稳健的原则，能够提供超越传统图表和数值摘要的丰富比较维度。通过案例研究，我们使用brms R包（斯坦贝叶斯建模的高级接口）拟合了五个贝叶斯分层模型，对PISA（国际学生评估项目）数据库中的国家数学成绩趋势进行建模。案例研究表明，遵循这些原则创建的可视化不仅能帮助研究者在贝叶斯分层模型结构间做出更明智的选择，还能有效传达其选择依据。