# Course Syllabus

## Course Title

Bayesian Statistics: From Foundations to Research Applications

## Course Description

This course introduces Bayesian statistics as a practical framework for learning from data under uncertainty. Students learn the logic of Bayesian inference, common probability models, conjugate analysis, simulation-based computation, MCMC, hierarchical modeling, Bayesian regression, model checking, decision analysis, and research reporting.

The course is applied but not software-only. Each topic starts with intuition and statistical reasoning, then moves to computation and interpretation.

## Learning Outcomes

Students who complete the course should be able to:

- Formulate Bayesian models from real research questions.
- Select and justify priors.
- Derive and interpret simple posterior distributions.
- Use simulation to estimate posterior summaries and uncertainty intervals.
- Fit Bayesian models with Python and PyMC.
- Diagnose MCMC output using trace plots, effective sample size, and R-hat.
- Use posterior predictive checks to evaluate model fit.
- Communicate Bayesian results for technical and non-technical audiences.

## Prerequisites

- Basic probability
- Descriptive statistics
- Introductory regression
- Beginner Python

## Assessment Plan

| Component | Weight |
|---|---:|
| Assignment 1: Foundations | 15% |
| Assignment 2: Conjugate models | 15% |
| Assignment 3: Monte Carlo and MCMC | 20% |
| Assignment 4: Hierarchical regression | 20% |
| Capstone project | 30% |

## Weekly Schedule

| Week | Lecture | Lab | Deliverable |
|---|---|---|---|
| 1 | Bayesian thinking | Probability and uncertainty review | Reflection memo |
| 2 | Conditional probability and Bayes theorem | Diagnostic testing examples | Practice problems |
| 3 | Priors, likelihoods, posteriors | Beta-binomial model | Assignment 1 |
| 4 | Conjugate models | Normal and Poisson examples | Model worksheet |
| 5 | Monte Carlo computation | Posterior simulation | Assignment 2 |
| 6 | MCMC | Diagnostics and interpretation | Lab report |
| 7 | Hierarchical models | Partial pooling | Assignment 3 |
| 8 | Bayesian regression | Linear and logistic models | Regression memo |
| 9 | Model checking | Posterior predictive checks | Model comparison |
| 10 | Decision analysis | Expected utility | Assignment 4 |
| 11 | Causal and time-series extensions | Research design discussion | Capstone proposal |
| 12 | Research workflow | Final presentation | Capstone report |

## Grading Rubric

Strong work should:

- Define the research question clearly.
- State the model assumptions.
- Explain the prior choice.
- Report posterior summaries and uncertainty intervals.
- Include model diagnostics when computation is used.
- Connect results back to the research problem.
- Use reproducible code and clean figures.

## Academic Integrity

Students may use software, documentation, and AI tools for learning, but all submitted work must show their own reasoning, code understanding, interpretation, and written explanation.

## Suggested References

- Statistical Rethinking by Richard McElreath
- Bayesian Data Analysis by Gelman et al.
- Doing Bayesian Data Analysis by John Kruschke
- PyMC documentation
- ArviZ documentation