Course Purpose
To develop theoretical understanding and practical competence in Bayesian inference, posterior analysis, model building, and decision-making under uncertainty.
Course Learning Outcomes
CLO 1: Understand the foundations and principles of Bayesian statistics.
CLO 2: Apply Bayes’ theorem and Bayesian estimation methods in statistical inference.
CLO 3: Implement Bayesian computational techniques including MCMC methods.
CLO 4: Develop, evaluate and interpret Bayesian models for practical applications.
Course Content
Part I: Foundations of Bayesian Statistics
Key Topics:
- Introduction to Bayesian statistics
- Bayesian philosophy
- Frequentist versus Bayesian approaches
- Applications of Bayesian inference
Part II: Probability and Bayes’ Theorem
Key Topics:
- Conditional probability
- Bayes’ theorem
- Random variables and probability distributions
- Likelihood functions
Part III: Bayesian Estimation and Conjugate Priors
Key Topics:
- Bayesian estimation
- Prior and posterior distributions
- Conjugate priors
- Posterior interpretation
Part IV: Bayesian Computation and MCMC Methods
Key Topics:
- Introduction to MCMC methods
- Metropolis-Hastings algorithm
- Gibbs sampling
- Convergence diagnostics
Part V: Bayesian Regression Models
Key Topics:
- Linear regression models
- Bayesian linear regression
- Posterior prediction
- Model interpretation
Part VI: Bayesian Model Diagnostics and Model Selection
Key Topics:
- Posterior predictive checks
- Model diagnostics
- Bayesian model comparison
- Information criteria
Part VII: Hierarchical Bayesian Models
Key Topics:
- Hierarchical modelling concepts
- Multilevel Bayesian models
- Hyperparameters
- Applications of hierarchical models
Part VIII: Advanced Bayesian Methods
Key Topics:
- Advanced sampling techniques
- Bayesian decision theory
- Approximate Bayesian computation
- Modern Bayesian applications
Part IX: Bayesian Model Selection and Uncertainty
Key Topics:
- Model uncertainty
- Bayesian model averaging
- Sensitivity analysis
- Decision making under uncertainty