Mathematics / advanced
Bayesian models and computation
Reason with prior information, likelihoods, posterior uncertainty, hierarchical structure, and calibrated computation.
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Module 01 advanced
Bayesian models and computation
Reason with prior information, likelihoods, posterior uncertainty, hierarchical structure, and calibrated computation.
- 01
Bayes' rule and prior predictive models
Construct a joint model, normalize its posterior, and check what the prior predicts before fitting observations.
32 min - 02
Conjugate families and posterior updating
Derive beta-binomial and gamma-Poisson updates while tracking normalization, units, and predictive dependence.
34 min - 03
Posterior loss and Bayes decisions
Turn posterior uncertainty into an action by specifying loss, comparing conditional risks, and checking sensitivity.
33 min - 04
Hierarchical models and partial pooling
Derive normal-model shrinkage, interpret exchangeability, and retain uncertainty in shared hyperparameters.
36 min - 05
Posterior predictive checking
Integrate parameter uncertainty, design revealing replicated-data summaries, and separate model checking from calibration.
35 min - 06
Marginal likelihood and Bayes factors
Compare fully specified predictive models while retaining normalizers, prior scales, and model odds.
35 min - 07
Importance sampling and effective sample size
Reweight independent proposal draws while checking support, tail behavior, ratio bias, and the limits of weight diagnostics.
37 min - 08
Metropolis–Hastings and detailed balance
Build a target-invariant transition kernel, retain rejected states, and separate stationarity from finite-run convergence.
38 min - 09
Hamiltonian Monte Carlo and diagnostics
Use auxiliary momentum and reversible integration while interpreting divergences, rank diagnostics, ESS, and Monte Carlo error.
40 min - 10
Variational inference and approximation error
Derive the ELBO, analyze a mean-field Gaussian example, and distinguish optimization success from posterior accuracy.
39 min