Bayesian Inference Fundamentals

Overview

AI, Data Science & Cloud Certificates from Google, IBM & Meta — 50% Off

One plan covers every Professional Certificate on Coursera. 50% off Coursera Plus Annual for 10 days only — price increases June 17.

Unlock All Certificates

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.

Syllabus

Introduction to Bayesian Inference Fundamentals

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.

Bayes' Theorem and Conjugate Priors

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.

Bayesian Estimation and Credible Intervals

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.

Markov Chain Monte Carlo (MCMC) Methods

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.