STAT 134 - Introduction to Bayesian Statistical Inference
Course Description
Overview and foundations of Bayesian analysis, assessment of prior
distributions, posterior distributions, and predictive distributions, Bayesian
inference, Bayesian hierarchical models, use of statistical software;
introduction to empirical Bayes.
Course Learning Outcomes
By the end of this course, the student must be able to:
- Identify the basic concepts of different prior and posterior
distributions;
- Differentiate between Bayesian and non-Bayesian framework;
- Demonstrate the role of prior information in Bayesian inference;
- Apply basic concepts in Bayesian modeling; and
- Interpret the results of Bayesian analysis.
Course Outline
UNIT 1. Introduction
- Overview of Bayesian Analysis
- Review of Probability
- Review of Inference
UNIT 2. Foundations
- Misuse of Classical Inference Procedures
- The Frequentist Perspective
- The Classical Perspective
- The Likelihood and Sufficiency Principle
UNIT 3. Bayes’ Theorem for Discrete and Continuous Models
- Prior Distribution
- Conjugate Priors
- Non-informative and Jeffrey’s Priors
- Predictive Distribution
- Posterior Distribution
UNIT 4. Bayesian Inference
- Bayesian Point Estimation
- Bayesian Confidence Sets
- Bayesian Hypothesis Testing
UNIT 5. Introduction to Hierarchical Models
- Definition of Hyperpriors and Hyperparameters
- Use of statistical software
UNIT 6. Introduction to Empirical Bayes
- Estimation of Hyperparameters
- Parametric Empirical Bayes
- Nonparametric Empirical Bayes