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 (known or unknown) variables (P), a posterior approximator (A), and training data (D). As an answer to the second question, we propose 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. Further, 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.

翻译：概率（贝叶斯）建模在几乎所有定量科学和工业领域都经历了应用激增。这一发展由多个因素共同驱动，包括更优的概率估计算法、灵活软件、计算能力提升，以及人们对概率学习优势认识的日益增强。然而，一套原则性的贝叶斯模型构建工作流程远未完善，仍面临诸多挑战。为助力未来原则性贝叶斯工作流程的研究与应用，我们提出并回答了我们认为贝叶斯建模的两个基本问题，即：(a) “贝叶斯模型究竟是什么？”和(b) “什么造就了好的贝叶斯模型？”。作为第一个问题的回答，我们提出了PAD模型分类法，该分类法定义了四种基本类型的贝叶斯模型，每种模型都代表了所有（已知或未知）变量的联合分布（P）、后验近似器（A）和训练数据（D）的某种组合。作为第二个问题的回答，我们提出了十个效用维度，据此我们可以全面评估贝叶斯模型，即：(1) 因果一致性、(2) 参数可恢复性、(3) 预测性能、(4) 公平性、(5) 结构忠实性、(6) 简约性、(7) 可解释性、(8) 收敛性、(9) 估算速度、(10) 鲁棒性。此外，我们提出了两个示例效用决策树，这些决策树描述了效用之间的层级关系和权衡取舍，具体取决于驱动模型构建和测试的推断目标。