Free online course Bayesian statistics: a comprehensive course
Duration of the online course: 5 hours and 3 minutes
New
Master Bayesian inference with this free statistics course—update beliefs with data, use priors smartly, and earn skills valued in analytics and research.
In this free course, learn about
Compute marginal densities from joint PDFs for continuous random variables
Compute conditional densities/probabilities for continuous RVs (e.g., P(X≤a|Y≤b))
Derive and apply Bayes’ rule; interpret what it updates (prior→posterior)
Use likelihood in Bayesian inference; distinguish likelihood from probability
Work with the Bayes denominator/evidence in discrete & continuous cases; when it cancels
Calculate posteriors in simple models (e.g., infection examples) and interpret results
Understand exchangeability, its definition, and relation to i.i.d. assumptions
Apply sequential Bayes updating; see why data order doesn’t matter under independence
Use MLE: set up and interpret maximum likelihood estimation for model parameters
Use conjugate priors and their benefits for closed-form posteriors
Beta-Bernoulli/Binomial modeling: parameters, posterior updates, gamma function role
Prior vs posterior predictive distributions; how hyperparameters affect predictions
Normal-Normal (known variance) conjugacy: posterior and predictive distributions intuition
Poisson-Gamma conjugacy: posterior and predictive (negative binomial) for count data
About the free online course
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.
Course content
Video class: 1 - Marginal probability for continuous variables06m
Exercise: What is the process to find the marginal probability of a continuous random variable?
Video class: 2 Conditional probability continuous rvs06m
Exercise: What is the probability of height ≤ 1.5m given weight ≤ 50kg?
Video class: A derivation of Bayes' rule02m
Exercise: What is Bayes' Rule derived from the given probabilities?
Video class: 4 - Bayes' rule - an intuitive explanation06m
Exercise: What does Bayes' Rule Help Determine?
Video class: 5 - Bayes' rule in statistics08m
Exercise: What is the ultimate goal of Bayesian statistics?
Video class: 6 - Bayes' rule in inference - likelihood07m
Exercise: What is the probability that all three individuals are uninfected given theta?
Video class: 7 Bayes' rule in inference the prior and denominator06m
Exercise: What is the likelihood probability for theta equals 0?
Video class: 8 - Bayes' rule in inference - example: the posterior distribution03m
Exercise: What is the posterior probability that Theta equals zero?
Video class: 9 - Bayes' rule in inference - example: forgetting the denominator04m
Exercise: Why can the denominator be ignored in Bayesian computations?
Video class: 10 - Bayes' rule in inference - example: graphical intuition05m
Exercise: What is the probability that theta equals 0 given the data and model choice?
Video class: 11 The definition of exchangeability04m
Exercise: What defines exchangeability in a sequence of random variables?
Video class: 12 exchangeability and iid07m
Exercise: What does exchangeability imply about random variables?
Video class: 13 exchangeability what is its significance?06m
Exercise: Why is exchangeability important in Bayesian statistics?
Video class: 14 - Bayes' rule denominator: discrete and continuous04m
Exercise: How is the denominator in the probability calculation determined in the context of Bayesian inference?
Video class: 15 Bayes' rule: why likelihood is not a probability04m
Exercise: Why shouldn't likelihood be considered identical to probability?
Video class: 15a - Maximum likelihood estimator - short introduction07m
Exercise: What is the primary goal of Maximum Likelihood Estimation?
Video class: 16 Sequential Bayes: Data order invariance04m
Exercise: What does Bayes' Rule imply about the order of independent data points?
Video class: 17 - Conjugate priors - an introduction05m
Exercise: What is a key advantage of using a conjugate prior in Bayesian inference?
Video class: 18 - Bernoulli and Binomial distributions - an introduction08m
Exercise: What is the purpose of the Bernoulli and binomial distributions?
Video class: 19 - Beta distribution - an introduction10m
Exercise: What is a key characteristic of the Beta distribution?
Video class: 20 - Beta conjugate prior to Binomial and Bernoulli likelihoods05m
Exercise: What are the parameters of a beta distribution?
Video class: 21 - Beta conjugate to Binomial and Bernoulli likelihoods - full proof05m
Exercise: What is the role of the gamma function in the proof of conjugate distributions?
Video class: 22 - Beta conjugate to Binomial and Bernoulli likelihoods - full proof 204m
Exercise: What is the conjugate prior for a Binomial distribution?
Video class: 23 - Beta conjugate to Binomial and Bernoulli likelihoods - full proof 302m
Exercise: What is demonstrated in the proof relating to the beta distribution and binomial likelihood?
Video class: 24 - Bayesian inference in practice - posterior distribution: example Disease prevalence07m
Exercise: What is a key advantage of having more data in a Bayesian inference model?
Video class: 25 - Bayesian inference in practice - Disease prevalence06m
Exercise: How does an increase in parameters 'a' and 'b' affect the posterior mean in Bayesian inference?
Video class: 26 - Prior and posterior predictive distributions - an introduction05m
Exercise: What is the difference between prior and posterior predictive distributions?
Video class: 27 - Prior predictive distribution: example Disease - 107m
Exercise: How does changing parameters affect the prior predictive distribution in the disease model?
Video class: 27 - Prior predictive distribution: example Disease - 206m
Exercise: What happens to the prior predictive distribution when a = b = 1?
Video class: 29 - Posterior predictive distribution: example Disease09m
Exercise: How does the posterior predictive probability change?
Video class: 30 - Normal prior and likelihood - known variance06m
Exercise: What is the mean of the professor's prior belief distribution?
Video class: 31 - Normal prior conjugate to normal likelihood - proof 105m
Exercise: What makes a normal prior density conjugate to a normal likelihood?
Video class: 32 - Normal prior conjugate to normal likelihood - proof 204m
Exercise: What is the result when a normal prior is conjugate to a normal likelihood when the variance is known?
Video class: 33 - Normal prior conjugate to normal likelihood - intuition07m
Exercise: What concept is illustrated by the effect of decreasing sigma θ²?
Video class: 34 - Normal prior and likelihood - prior predictive distribution06m
Exercise: What is the mean of the prior predictive distribution for the test score?
Video class: 35 - Normal prior and likelihood - posterior predictive distribution05m
Exercise: What is the posterior predictive distribution with a normal prior and likelihood?
Video class: 36 - Population mean test score - normal prior and likelihood08m
Exercise: What happens to the posterior distribution when more data is collected?
Video class: 37 - The Poisson distribution - an introduction - 109m
Exercise: What is necessary for events to be modeled by Poisson distribution?
Video class: 38 - The Poisson distribution - an introduction - 210m
Exercise: What is the mean of a Poisson distribution?
Video class: 39 - The gamma distribution - an introduction17m
Exercise: What is the mean of a Gamma distribution with parameters α and β?
Video class: 40 - Poisson model: crime count example introduction05m
Exercise: What is a key assumption for using the Poisson model in the described scenario?
Video class: 41 - Proof: Gamma prior is conjugate to Poisson likelihood08m
Exercise: When is a Gamma prior conjugate to a Poisson likelihood?
Video class: 42 - Prior predictive distribution for Gamma prior to Poisson likelihood07m
Exercise: What is the distribution derived from a gamma prior and Poisson likelihood?
Video class: 43 - Prior predictive distribution (a negative binomial) for gamma prior to poisson likelihood 207m
Exercise: What is the result of using a gamma prior with a Poisson likelihood in deriving the prior predictive distribution?
Video class: 44 - Posterior predictive distribution a negative binomial for gamma prior to poisson likelihood11m
Exercise: What is the nature of the posterior predictive distribution given a Poisson likelihood and gamma prior?
