Chapter-by-chapter expansion map

How to read this map

The detailed chapter expansion outlines are organized by course part:

Each part page is written as an expansion-ready authoring brief. For every chapter it lists:

  • core questions;
  • formal topics and definitions;
  • derivations that must be shown in detail;
  • computational labs and software targets;
  • diagnostics and common pitfalls;
  • exercises and reading suggestions.

Status of content in this repository

Chapter Status in this repository Location
1-2 Fully written chapters Part I chapters
3 Fully written sample chapter Bayes theorem chapter
4-6 Fully written chapters Part II chapters
7 Fully written chapter Numerical integration chapter
8 Fully written chapter Monte Carlo chapter
9 Fully written sample chapter MCMC chapter
10-12 Fully written chapters Part III chapters
13-20 Fully written chapters Part IV chapters
21-23 Fully written chapters Part V chapters
24-26 Fully written chapters Part VI chapters
27-31 Fully written chapters Part VII chapters

Authoring convention

To extend existing chapters or add future textbook-style chapters, retain the following section order whenever it fits the material:

  1. Chapter introduction and learning outcomes.
  2. Motivation and intuition.
  3. Formal setup and notation.
  4. Main result or model structure.
  5. Step-by-step derivation.
  6. Worked analytic example.
  7. Computational implementation.
  8. Diagnostics and failure modes.
  9. Exercises with solution sketches.
  10. References and further reading.

Cross-cutting themes to preserve

As the site grows, every chapter should remain aligned with five global themes:

Mathematical precision

Definitions and assumptions should be explicit. Approximation methods should always state the object being approximated and the mode of approximation error.

Workflow discipline

Every model chapter should include some version of:

  • prior design;
  • posterior computation;
  • predictive checking;
  • sensitivity analysis;
  • reporting.

Computational transparency

When algorithms are introduced, the course should state:

  • target distribution;
  • transition rule or optimization objective;
  • tuning parameters;
  • computational cost;
  • known pathologies.

Reproducibility

Every substantial code example should have a corresponding source file in labs/, or a direct path for students to reproduce it.

Comparative reasoning

Students should repeatedly compare:

  • likelihood vs posterior inference;
  • optimization vs integration;
  • MCMC vs VI;
  • exact conjugate inference vs numerical approximation;
  • prediction vs explanation vs decision.

Immediate reading paths

Different audiences can enter the material through different routes.

Statistically mature reader

Start with:

  1. Part III: Computation
  2. MCMC chapter
  3. Stan workflow chapter
  4. Diagnostics section in Part V

Applied modeler

Start with:

  1. Part II: Core Bayesian Inference
  2. Part IV: Models
  3. Part VI: Software Workflows

Theory-oriented reader

Start with:

  1. Part I: Foundations
  2. Bayes theorem chapter
  3. Part II: Core Bayesian Inference
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