Free online courseBayesian statistics: a comprehensive course

Course Description

Bayesian thinking changes how you interpret uncertainty: instead of treating parameters as fixed and data as random, you learn to update what you believe as evidence accumulates. This free online course is designed to help you build that mindset and apply it confidently to real statistical questions, even if Bayes’ rule has felt abstract in the past. By the end, you should be able to move from intuition to calculation and explain, in plain language, what your posterior conclusions mean and why they follow from your assumptions.

You’ll start by strengthening the probability foundations that make Bayesian methods work, especially marginal and conditional probability for continuous variables. From there, Bayes’ rule becomes more than a formula: it becomes a practical tool for reasoning. You will see how the likelihood connects models to data, why it is not the same thing as a probability statement about parameters, and how priors shape conclusions without turning analysis into guesswork. You will also learn why, in many computations, a messy normalizing denominator can be set aside temporarily while still arriving at the correct posterior form.

A key feature of Bayesian modeling is recognizing when assumptions are justified. That’s why the course emphasizes ideas like exchangeability and its relationship to iid thinking, giving you a clearer rationale for common modeling shortcuts. You’ll also explore sequential updating and why, under standard conditions, the order of independent data points should not change your inference—an insight that reinforces both correctness and intuition.

To make Bayesian inference actionable, the course highlights conjugate priors as a fast, interpretable pathway to posterior distributions. You’ll work through classic families such as Beta-Binomial for proportions, Normal-Normal for means (with known variance), and Gamma-Poisson for count data, connecting each choice to practical scenarios like disease prevalence, test scores, and event counts. Predictive thinking is woven throughout, helping you go beyond estimating parameters to forecasting what future observations may look like under both prior and posterior beliefs.

Whether you are a student in school subjects, a beginner aiming for confidence in statistics, or someone preparing for data-focused roles, this course helps you build reliable reasoning habits. You will finish with a clearer grasp of how to express uncertainty, defend modeling choices, and turn data into updated, decision-ready conclusions.