Bayesian statistics
Undergraduate · Statistics
Syllabus focus
Standard syllabus · Theoretical / proof-based
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$60.00 · 60 min · Undergraduate · Online ($60/hr)
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Topics typically covered
Standard syllabus
Bayesian foundations
- Subjective probability and Bayes' theorem
- Prior, likelihood, and posterior
- Conjugate priors: beta-binomial, normal-normal
- Credible intervals vs confidence intervals
- Bayesian hypothesis testing (introduction)
Computation and models
- Posterior simulation: Monte Carlo methods
- Introduction to MCMC: Metropolis–Hastings and Gibbs
- Bayesian linear and logistic regression
- Model comparison: Bayes factors (intro)
- Sensitivity to prior choice
Applications
- Hierarchical models (introduction)
- Empirical Bayes methods
- Bayesian model averaging (overview)
- Communicating posterior uncertainty
Theoretical / proof-based
Decision and estimation theory
- Bayes estimators and admissibility
- Loss functions and posterior risk
- Minimax and Bayes connections
- Jeffreys priors and reference priors
- Bernstein–von Mises theorem (statement)
- Proofs for conjugate posterior updates
Additional applied practice
- Reviewing assumptions with domain experts
- Documenting analysis choices for reproducibility
- Sensitivity analyses for key modeling decisions
- Connecting results to the original research or business question
Notes
Undergraduate Bayesian courses range from conceptual introductions to computation-heavy offerings. Theoretical sections include decision theory and conjugate families with derivations.