Bayesian Workflow - Overview

Summary

Bayesian workflow extends far beyond Bayesian inference ($p(\theta |y)\propto p(\theta )p(y|\theta )$). It encompasses the full iterative cycle of model building, fitting, checking, and revision that characterizes real applied Bayesian data analysis. This paper by Gelman, Vehtari, Simpson, Margossian, Carpenter, Yao, Kennedy, Gabry, Burkner, and Modrak (2020) codifies the tacit knowledge practitioners need.

Workflow vs. Inference

Bayesian inference is the computation of conditional probabilities or posterior densities. Bayesian workflow includes the three steps of model building, inference, and model checking/improvement, along with the comparison of different models — not just for model choice but to better understand each model’s behavior.

The authors emphasize that in practice we fit many models for any given problem, and even poor models serve as unavoidable steps along the way toward fitting useful ones.

Why a Workflow Is Needed

1. Computation is hard — we must work through various steps including simpler models and approximate computation to reach trustworthy inferences.
2. We rarely know the final model ahead of time — models expand as we gather data and ask more detailed questions.
3. Data are often not fixed — new data require model extensions and re-evaluation.
4. Understanding requires comparison — models are best understood by comparing inferences across a series of related models.

The Iterative Cycle

The workflow follows a non-linear path (see Figure 1 of the paper):

1. Pick an initial model (Choosing and Building Models)
2. Prior predictive check to validate priors against domain knowledge
3. Fit the model (Fitting and Validating Computation)
4. Validate computation — convergence diagnostics, fake-data simulation, SBC
5. Address computational issues if needed (Computational Troubleshooting)
6. Evaluate and use the model (Evaluating Fitted Models)
7. Modify the model (Iterative Model Improvement)
8. Compare models across the topology of fitted models

Connection to Statistical Methodology

The paper frames methodology development as a progression: Example → Case study → Workflow → Method → Theory. Workflows are more general than examples but less precisely specified than formal methods, filling an important gap in the literature.

Related Notes

• Choosing and Building Models
• Fitting and Validating Computation
• Computational Troubleshooting
• Evaluating Fitted Models
• Iterative Model Improvement
• Modeling as Software Development
• Model Checking | Model Comparison | MCMC Basics

See Also (Cross-Domain)

• BDA3 - Overview — the textbook that provides the theoretical foundation for this workflow
• Forking Paths and Bayesian Approaches — workflow as a defense against multiple comparisons problems
• The Experimental Ideal — how Bayesian workflow complements careful experimental design
• Regression and the CEF — workflow applies equally to Bayesian regression for causal inference
• Overfitting and Information Criteria — WAIC and LOO-CV are the quantitative tools for the model comparison step in the workflow
• ABM Calibration Overview — ABM calibration/validation follows an analogous iterative cycle (simulate → calibrate → validate → improve), with history matching and ABC playing roles parallel to prior predictive checking and model assessment