Bayesian statistics
Graduate · Math
Syllabus focus
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Graduate Bayesian statistics — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable).
Bayesian foundations
- Coherent inference — Coherent inference
- Dutch book arguments (intro) — Dutch book arguments (intro)
- Prior construction: conjugate, Jeffreys, reference — Prior construction: conjugate, Jeffreys, reference
- Posterior asymptotics: Bernstein–von Mises — Posterior asymptotics: Bernstein–von Mises
- Bayes factors and model selection — Bayes factors and model selection
- Decision theory: Bayes rules — Decision theory: Bayes rules
- Admissibility — Admissibility
Computation
- Monte Carlo integration — Monte Carlo integration
- Importance sampling — Importance sampling
- MCMC: Metropolis–Hastings, Gibbs, HMC (overview) — MCMC: Metropolis–Hastings, Gibbs, HMC (overview)
- Convergence diagnostics: R-hat, effective sample size — Convergence diagnostics: R-hat, effective sample size
- Variational inference (introduction) — Variational inference (introduction)
- Approximate Bayesian computation (ABC) — Approximate Bayesian computation (ABC)
Hierarchical modeling
- Exchangeability — Exchangeability
- Hierarchical priors — Hierarchical priors
- Empirical Bayes and hyperpriors — Empirical Bayes and hyperpriors
- Spatial — Spatial
- Spatiotemporal Bayes models (intro) — Spatiotemporal Bayes models (intro)
- Nonparametric Bayes: Dirichlet process (overview) — Nonparametric Bayes: Dirichlet process (overview)
- Sensitivity analysis — Sensitivity analysis
- Robust priors — Robust priors
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Bayesian foundations
Coherent inference
Coming soon - Computation
Monte Carlo integration
Coming soon - Hierarchical modeling
Exchangeability
Coming soon
Notes
Graduate Bayesian statistics — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable). Topic outline: `content/topics/graduate/bayesian_grad.json`.