Bayesian Inference Fundamentals
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Bayesian Inference Fundamentals
This course is part of Applied Bayesian Data Analysis Specialization
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What you'll learn
Apply Bayes' theorem to compute posterior distributions and quantify uncertainty in statistical inference problems.
Explain conjugacy for efficient Bayesian inference and interpret credible intervals for parameter estimation.
Compare Bayesian and frequentist approaches to understand philosophical differences in statistical reasoning.
Execute MCMC algorithms, including Metropolis-Hastings and Gibbs sampling, for complex posterior approximation.
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May 2026
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There are 4 modules in this course
Master Bayesian inference and unlock powerful probabilistic reasoning for data-driven decision-making. This course builds your foundation in Bayesian analysis, from viewing probability as degrees of belief to implementing advanced MCMC methods. Learn to apply Bayes’ theorem to real-world problems, use conjugate priors for efficient computation, and derive credible intervals that fully capture parameter uncertainty. Through hands-on practice, you’ll move from analytical solutions to computational techniques like Metropolis-Hastings, Gibbs sampling and Variational Inference, essential for modern Bayesian workflows. You’ll gain skill in interpreting posterior distributions, contrasting Bayesian and frequentist perspectives, and applying convergence diagnostics for reliable results. Whether in finance, healthcare, or business, you’ll acquire the statistical framework and computational tools to make principled inferences under uncertainty and effectively communicate probabilistic insights.
Welcome to Bayesian Inference Fundamentals! In this module, you will be introduced to the Bayesian way of thinking. First, focusing on the qualitative and quantitative details of Bayes' theorem. Then, you will also learn about random variables, which are a central piece of probabilistic and Bayesian analysis.
What's included
5 videos7 readings5 assignments1 ungraded lab
5 videos•Total 23 minutes
- Introduction to Bayesian Thinking•3 minutes
- Probabilistic Thinking•6 minutes
- Conditional Probability and Bayes' Rule•4 minutes
- The Prior•5 minutes
- Random Variables•4 minutes
7 readings•Total 70 minutes
- Course Overview•10 minutes
- Technical and Accessibility Support•5 minutes
- The McGurk Effect•20 minutes
- Bayesian Average•10 minutes
- Disease Testing and Bayes' Rule•10 minutes
- Module Wrap-Up•5 minutes
- Recommended Learning Resources•10 minutes
5 assignments•Total 90 minutes
- Lab Check-in: Bayesian Inference in College Football•5 minutes
- Probabilities and Beliefs•10 minutes
- Bayesian Reasoning & Uncertainty•15 minutes
- Test Yourself: Introduction to Applied Bayesian Data Analysis•30 minutes
- Let's Practice: Introduction to Applied Bayesian Data Analysis•30 minutes
1 ungraded lab•Total 45 minutes
- Guided Lab: Bayesian Inference in College Football•45 minutes
In this module, you will further your understanding of Bayes’ rule by applying it to distributions of random variables. This will provide you with the full benefits of the Bayes rule, going beyond posterior point estimates.
What's included
6 videos3 readings7 assignments1 ungraded lab
6 videos•Total 22 minutes
- Foundations of Bayesian Inference•2 minutes
- Bayes’ Rule Beyond Point Estimates•4 minutes
- Bayesian NFL player evaluation•5 minutes
- Conjugate Priors•4 minutes
- Sequential updates in Python•3 minutes
- Laplacian smoothing•4 minutes
3 readings•Total 40 minutes
- Normal, Binomial, and, Poisson distributions•20 minutes
- Poisson Likelihood•15 minutes
- Module Wrap-Up •5 minutes
7 assignments•Total 119 minutes
- Bayes' Rule for Distributions•10 minutes
- A deeper look at the Bayesian NFL player evaluation•30 minutes
- Conjugate priors•10 minutes
- Lab Check-in: Bayesian Box Office Revenue•5 minutes
- Laplacian Smoothing•4 minutes
- Test Yourself: Bayes' Theorem and Conjugate Priors•30 minutes
- Let's Practice: Bayes' Theorem and Conjugate Priors•30 minutes
1 ungraded lab•Total 60 minutes
- Bayesian Box Office Revenue•60 minutes
In this module, you will focus on the important difference between the Bayesian and frequentist approaches through the lens of credible and confidence intervals. You will understand the main benefits of taking a Bayesian approach in analyzing your data, and you will see a first set of methods for approximating posteriors through simulations.
What's included
5 videos5 readings6 assignments2 ungraded labs
5 videos•Total 16 minutes
- Credible intervals•3 minutes
- Credible vs confidence intervals•3 minutes
- Posterior sampling•3 minutes
- Approximate Bayesian Computation (ABC)•4 minutes
- Rejection Sampling•4 minutes
5 readings•Total 100 minutes
- Empirical Credible Intervals•45 minutes
- Inverse Transform Sampling•10 minutes
- ABC Example: The importance of function S()•10 minutes
- An example of how to sample like a snob: reject them•30 minutes
- Module Wrap-Up •5 minutes
6 assignments•Total 110 minutes
- Is it credible or is it confident?•10 minutes
- Sampling•10 minutes
- Simulation-based Methods•15 minutes
- Roll the dice and test your sampling knowledge•15 minutes
- Test Yourself: Bayesian Estimation and Credible Intervals•30 minutes
- Let's Practice: Bayesian Estimation and Credible Intervals•30 minutes
2 ungraded labs•Total 120 minutes
- Highest Density Intervals (HDIs) Demonstration•60 minutes
- Rejection Sampling Particle•60 minutes
In this module, we will introduce the core of Bayesian inference, Markov Chain Monte Carlo. We will see in detail two foundational algorithms in Gibbs sampling and Metropolis-Hastings sampling. We will also identify best practices and diagnostics for convergence.
What's included
4 videos5 readings5 assignments2 ungraded labs
4 videos•Total 18 minutes
- Markov Chain Monte Carlo (MCMC)•4 minutes
- Gibbs Sampling•4 minutes
- Metropolis-Hastings Sampling•4 minutes
- MCMC Convergence•5 minutes
5 readings•Total 68 minutes
- Why do we need MCMC?•10 minutes
- Bayesian inference with Metropolis-Hastings sampling•35 minutes
- Other Sampling Algorithms•10 minutes
- Module Wrap-Up •3 minutes
- Course Summary•10 minutes
5 assignments•Total 100 minutes
- MCMC Method•10 minutes
- Lab Check-in: Gibbs sampling in Python•5 minutes
- MCMC Algorithms•25 minutes
- Test Yourself: Markov Chain Monte Carlo (MCMC) Methods•30 minutes
- Let's Practice: Markov Chain Monte Carlo (MCMC) Methods•30 minutes
2 ungraded labs•Total 120 minutes
- Gibbs sampling in Python•60 minutes
- Metropolis Hastings Bayesian inference•60 minutes
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