Foundations of Bayesian Computational Statistics

How do we update our beliefs as new data arrives? Bayesian computational statistics provides the mathematical and practical framework to model uncertainty and make highly informed predictions. This text-only course guides you from the fundamental principles of probability to writing and evaluating your first Bayesian models. You will learn how to transition from traditional frequentist thinking to a Bayesian mindset, utilizing modern computational tools to solve real-world data challenges. What you'll learn: Understand the core mathematical concepts of prior, likelihood, and posterior distributions; Apply Bayesian inference techniques to estimate parameters and make predictions; Explore modern computational algorithms including Markov Chain Monte Carlo (MCMC) methods; Build and evaluate probabilistic models using contemporary coding practices; Interpret model diagnostics to ensure the reliability and accuracy of your statistical analysis. The course begins with foundational probability concepts and key terminology before moving into practical modeling scenarios, diagnostic workflows, and modern computational implementations. Designed for beginners in data science and statistics, this course requires only basic algebra and a general familiarity with data concepts—no prior advanced statistics experience is needed. Start your journey into Bayesian analysis and discover a more intuitive way to work with uncertainty.