Bayesian Statistics Lecture by Jingchen Hu

About this course

Bayesian statistics gives you a practical way to reason with uncertainty, combine prior knowledge with data, and communicate results as probabilities people actually understand. In this free online course, you will build intuition and skill from the ground up: how to interpret probability, apply Bayes’ rule, and move from basic calculations to modern Bayesian inference workflows used across science, business, and public policy.

You will learn how to update beliefs with data using conjugate models, beginning with proportions and the Beta distribution, then moving to inference for means and variability in Normal models. Along the way, you will practice translating real questions into likelihoods, choosing priors that reflect what is known (or intentionally vague), and interpreting posterior summaries and credible intervals in a way that supports clear decision-making.

Not every posterior distribution is easy to compute analytically, so the course also develops computational tools to approximate posterior quantities. You will use Monte Carlo methods to estimate probabilities of comparisons and effects, and then step into MCMC with Gibbs sampling and Metropolis-Hastings, including guidance on diagnosing convergence and assessing whether your simulation is reliable. You will also work with JAGS to fit models and extract Bayesian inferences, gaining exposure to how probabilistic models are specified in practice.

From there, the course broadens into hierarchical modeling, showing how partial pooling can stabilize estimates when data are grouped or sparse, while still preserving meaningful differences between groups. You will see how hierarchical Bayesian models naturally address real-world structure, and you will connect these ideas to regression modeling, including simple and multiple linear regression with priors that match standardized predictors and interpretable effects.

Throughout, you will reinforce learning with labs, exercises, and applied prompts that mirror the thinking needed for a Bayesian project: defining a question, building a model, checking it, and reporting conclusions responsibly. By the end, you will be prepared to read and implement Bayesian analyses, justify modeling choices, and extend your toolkit toward advanced topics such as variational inference and modern applied case studies.