This course equips learners with the theoretical knowledge and computational skills needed to implement modern Bayesian statistical methods in real-world settings. By completing the course, learners will be able to build and fit Bayesian models, apply computational algorithms for posterior inference, and interpret uncertainty in complex data analysis problems. Topics include maximum a posteriori (MAP) estimation, rejection sampling, and Markov chain Monte Carlo (MCMC) methods such as the Gibbs sampler and Metropolis-Hastings algorithms. Learners will also gain hands-on experience using Stan, one of the leading platforms for Bayesian modeling and probabilistic programming.

The course is designed for learners seeking to strengthen their statistical, machine learning, and data science capabilities in industry or research settings. Bayesian methods are increasingly used in areas such as AI, forecasting, experimentation, risk analysis, and decision-making under uncertainty. Unlike many applied courses that focus primarily on software tools, this course emphasizes both the mathematical foundations and computational intuition underlying modern Bayesian workflows, helping learners develop a deeper understanding of how and why these methods work. This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the MS-DS is ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://coursera.netlol.uk/degrees/master-of-science-data-science-boulder.