Theoretical / proof-based
Bayesian statistics · Graduate · Math
Learning objectives from the Bayesian statistics syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
Click a topic for the full text and related unit practice.
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
Learning objectives
Click an objective for study materials.
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
Definitions and structure
- 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
Proofs and reasoning
- Decision theory: Bayes rules — Decision theory: Bayes rules
- Admissibility — Admissibility
- Monte Carlo integration — Monte Carlo integration
- Importance sampling — Importance sampling
- MCMC: Metropolis–Hastings, Gibbs, HMC (overview) — MCMC: Metropolis–Hastings, Gibbs, HMC (overview)
Abstraction and generalization
- 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)
- Exchangeability — Exchangeability
- Hierarchical priors — Hierarchical priors
Modeling and computation
- Apply coherent inference in engineering contexts — Apply coherent inference in engineering contexts
- Apply dutch book arguments (intro) in engineering contexts — Apply dutch book arguments (intro) in engineering contexts
- Apply prior construction: conjugate, jeffreys, reference in engineeri... — Apply prior construction: conjugate, jeffreys, reference in engineering contexts
- Apply posterior asymptotics: bernstein–von mises in engineering contexts — Apply posterior asymptotics: bernstein–von mises in engineering contexts
- Apply bayes factors and model selection in engineering contexts — Apply bayes factors and model selection in engineering contexts
Data and technology
- Use software to explore bayesian statistics problems numerically — Use software to explore bayesian statistics problems numerically
- Interpret computational results against analytic predictions — Interpret computational results against analytic predictions
- Build spreadsheets or scripts for routine calculations — Build spreadsheets or scripts for routine calculations
- Visualize functions, fields, or datasets tied to course topics — Visualize functions, fields, or datasets tied to course topics
- Connect course methods to lab, industry, or research workflows — Connect course methods to lab, industry, or research workflows
Problem-solving practice
- Decision theory: Bayes rules — Decision theory: Bayes rules
- Admissibility — Admissibility
- Monte Carlo integration — Monte Carlo integration
- Importance sampling — Importance sampling
- MCMC: Metropolis–Hastings, Gibbs, HMC (overview) — MCMC: Metropolis–Hastings, Gibbs, HMC (overview)
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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