Index: Simulation-Based Calibration

Simulation-Based Calibration

Routing Summary

Chapter 14 of Gelman, Vehtari & McElreath (2026) — SBC as an integrated workflow step rather than a standalone validation ritual. 1 note here; the theory lives in the Talts et al. (2018) notes at the parent folder level and the worked debugging session lives in Case Studies.

• Need SBC’s place in the workflow, the $\gamma$ metric, and when to run it? → SBC in the Workflow
• Need the foundational identity (prior = data-averaged posterior)? → Data-Averaged Posterior Self-Consistency
• Need the rank statistic and uniformity theorem? → Rank Statistics and Uniformity
• Need the step-by-step algorithm? → The SBC Algorithm
• Need to read histogram shapes (∪, ∩, sloped)? → Interpreting SBC Histograms
• Need worked examples from the original paper (HMC/ADVI/INLA, eight schools)? → SBC Case Studies
• Need a full debugging session with five real bugs? → Simulation-Based Calibration Checking in Model Development Workflow

Concept Map

Concept	Note	Type	Depends On	Key Result
SBC as a workflow step	SBC in the Workflow	concept	The SBC Algorithm	Eq. 14.1; Figures 14.1–14.4; the $\gamma$ metric; where SBC fits between model specification and fitting to real data
Data-averaged posterior identity	Data-Averaged Posterior Self-Consistency	theorem	—	$\int p(\theta \mid y)p(y)dy=p(\theta )$
Rank uniformity	Rank Statistics and Uniformity	theorem	Data-Averaged Posterior Self-Consistency	Ranks of prior draws among posterior draws are uniform
The algorithm	The SBC Algorithm	concept	Rank Statistics and Uniformity	Algorithms 1 and 2
Histogram diagnosis	Interpreting SBC Histograms	concept	The SBC Algorithm	∪ = overdispersed, ∩ = underdispersed, sloped = biased
Debugging with SBC	Simulation-Based Calibration Checking in Model Development Workflow	example	SBC in the Workflow	Five bugs found; data-only filtering preserves the SBC identity

Notes

• SBC in the Workflow — CONTAINS: Eq. 14.1; Figures 14.1–14.4; the $\gamma$ metric; SBC’s cost and when it is worth paying; Ch. 14 of the book

From Talts et al. (2018), stored one level up — complementary theory, not superseded:

• Simulation-Based Calibration - Overview — CONTAINS: the method at a glance
• Data-Averaged Posterior Self-Consistency — CONTAINS: the foundational identity
• Rank Statistics and Uniformity — CONTAINS: the uniformity theorem
• The SBC Algorithm — CONTAINS: Algorithms 1 and 2
• Interpreting SBC Histograms — CONTAINS: histogram shape diagnosis, autocorrelation handling
• SBC Case Studies — CONTAINS: HMC/ADVI/INLA comparisons, eight schools

Sources

• Gelman Vehtari McElreath 2026 - Bayesian Workflow (book) — Chapter 14, pp. 249–254
• 1804.06788-Talts-SBC — the original SBC paper

See Also

• Simulation-Based Calibration Checking in Model Development Workflow — Chapter 31, the worked case study
• Computational Workflow — convergence diagnostics, which SBC complements
• Designing Simulated-Data Experiments — the broader family of simulated-data checks