Open Access
2023 Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy
Paul-Christian Bürkner, Maximilian Scholz, Stefan T. Radev
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Statist. Surv. 17: 216-310 (2023). DOI: 10.1214/23-SS145


Probabilistic (Bayesian) modeling has experienced a surge of applications in almost all quantitative sciences and industrial areas. This development is driven by a combination of several factors, including better probabilistic estimation algorithms, flexible software, increased computing power, and a growing awareness of the benefits of probabilistic learning. However, a principled Bayesian model building workflow is far from complete and many challenges remain. To aid future research and applications of a principled Bayesian workflow, we ask and provide answers for what we perceive as two fundamental questions of Bayesian modeling, namely (a) “What actually is a Bayesian model?” and (b) “What makes a good Bayesian model?”. As an answer to the first question, we propose the PAD model taxonomy that defines four basic kinds of Bayesian models, each representing some combination of the assumed joint distribution of all observable and unobservable variables (P), a posterior approximator (A), and training data (D). As an answer to the second question, we propose and discuss ten utility dimensions according to which we can evaluate Bayesian models holistically, namely, (1) causal consistency, (2) parameter recoverability, (3) predictive performance, (4) fairness, (5) structural faithfulness, (6) parsimony, (7) interpretability, (8) convergence, (9) estimation speed, and (10) robustness. Finally, we propose two example utility decision trees that describe hierarchies and trade-offs between utilities depending on the inferential goals that drive model building and testing.


We thank Rudolf Debelak for helpful feedback on earlier versions of this paper. Our work was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2075 - 390740016 (the Stuttgart Cluster of Excellence SimTech) and EXC-2181 - 390900948 (the Heidelberg Cluster of Excellence STRUCTURES). The authors gratefully acknowledge the support and funding.


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Paul-Christian Bürkner. Maximilian Scholz. Stefan T. Radev. "Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy." Statist. Surv. 17 216 - 310, 2023.


Received: 1 October 2022; Published: 2023
First available in Project Euclid: 26 November 2023

Digital Object Identifier: 10.1214/23-SS145

Primary: 62–02
Secondary: 62C10

Keywords: Bayesian statistics , machine learning , model comparison , Probabilistic modeling , Statistical learning

Vol.17 • 2023
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