Bayesian Statistics: From Foundations to Research Applications

Complete open course for students, researchers, and applied data scientists who want to learn Bayesian statistics from first principles and use it in real research workflows.

This course is designed by Mahbub Hassan for self-study, classroom teaching, and research-lab training. It emphasizes intuition, mathematical reasoning, computational practice, and reproducible applied analysis.

Course Goals

By the end of this course, learners should be able to:

• Explain Bayesian thinking using priors, likelihoods, posteriors, and posterior predictive distributions.
• Build conjugate Bayesian models for proportions, rates, means, and uncertainty estimation.
• Use Monte Carlo simulation and Markov chain Monte Carlo for models without closed-form solutions.
• Fit Bayesian regression and hierarchical models with Python.
• Diagnose convergence, interpret uncertainty, and communicate posterior results clearly.
• Compare models using predictive checks and information criteria.
• Design a complete Bayesian research project from problem statement to final report.

Who This Course Is For

• Undergraduate and graduate students in statistics, engineering, transportation, economics, public health, social science, and data science.
• Researchers who use quantitative methods and want stronger uncertainty reasoning.
• Machine learning practitioners who want probabilistic modeling skills.
• Students preparing for thesis, journal paper, or research assistant work.

Recommended Background

Learners should know basic algebra, probability, and Python. Prior exposure to regression helps, but the course reviews the needed foundations.

Course Structure

Week	Module	Main Outcome
1	Bayesian Thinking	Understand Bayesian reasoning and uncertainty
2	Probability Review	Use probability rules needed for Bayesian modeling
3	Priors, Likelihoods, and Posteriors	Translate research questions into Bayesian models
4	Conjugate Models	Solve beta-binomial, gamma-Poisson, and normal models
5	Monte Carlo Computation	Approximate posterior quantities with simulation
6	MCMC	Understand sampling, chains, diagnostics, and convergence
7	Hierarchical Models	Model grouped data with partial pooling
8	Bayesian Regression	Fit linear, logistic, and count regression models
9	Model Checking and Comparison	Evaluate models with posterior predictive checks
10	Decision Analysis	Connect posterior inference to decisions
11	Causal and Time-Series Extensions	Extend Bayesian thinking to advanced applied questions
12	Capstone Workflow	Complete a reproducible Bayesian research project

Labs

Lab	Topic	File
1	Beta-binomial updating	lab01_beta_binomial.py
2	Normal-normal updating	lab02_normal_normal.py
3	Monte Carlo integration	lab03_monte_carlo.py
4	MCMC diagnostics	lab04_mcmc_diagnostics.py
5	Hierarchical modeling	lab05_hierarchical_model.py
6	Bayesian regression workflow	lab06_bayesian_regression.py

Assignments

• Assignment 1: Bayesian Foundations
• Assignment 2: Conjugate Modeling
• Assignment 3: Monte Carlo and MCMC
• Assignment 4: Hierarchical Regression
• Capstone Project

Quick Start

Clone the repository:

git clone https://github.com/mahbubchula/bayesian-statistics-course.git
cd bayesian-statistics-course

Create a Python environment:

python -m venv .venv
.venv\Scripts\activate
pip install -r requirements.txt

Run a lab:

python labs/lab01_beta_binomial.py

Software

Core tools:

• Python
• NumPy
• pandas
• SciPy
• Matplotlib
• ArviZ
• PyMC

PyMC is used for applied Bayesian modeling. The early modules are written so learners can understand the statistics before relying on software.

Datasets

Small teaching datasets are included in the datasets folder:

• coin_quality.csv: binary quality-control data for beta-binomial modeling
• traffic_wait_times.csv: waiting-time data for normal and hierarchical models
• ev_adoption_sample.csv: simple applied dataset for Bayesian regression

These datasets are synthetic teaching data and should not be interpreted as real-world measurements.

Suggested Teaching Format

For a 12-week course:

• 1 lecture per week
• 1 lab or tutorial per week
• 4 graded assignments
• 1 final capstone project

For a short workshop:

• Day 1: Modules 1 to 4
• Day 2: Modules 5 to 8
• Day 3: Modules 9 to 12 and capstone planning

Repository Map

bayesian-statistics-course/
  README.md
  syllabus.md
  index.html
  requirements.txt
  modules/
  labs/
  assignments/
  datasets/
  slides/
  assets/

Citation

If you use this course in teaching or training, please cite the repository:

Mahbub Hassan. Bayesian Statistics: From Foundations to Research Applications. GitHub repository, 2026.

License

Course text, assignments, and teaching materials are released under the Creative Commons Attribution 4.0 International License. Code examples are released under the MIT License.