Overview

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Master advanced Bayesian inference techniques and their practical applications in data science. This course will equip you with cutting-edge methods, including variational inference, Bayesian decision theory, and non-parametric approaches. You'll learn to quantify uncertainty in predictions, make principled decisions using loss functions, and implement flexible models that adapt complexity to data. Through hands-on projects using PyMC3 and real-world case studies, you'll develop expertise in the complete Bayesian workflow: from model specification to validation. The course emphasizes scalable alternatives to MCMC, including variational inference for large datasets, and covers advanced topics such as Dirichlet processes and Gaussian process regression. What makes this course unique is its focus on practical implementation and decision-making under uncertainty. You'll gain skills in probabilistic programming, model evaluation, and applying Bayesian methods to diverse domains. By completing this course, you'll be equipped to tackle complex data problems with rigorous statistical methods and communicate uncertainty effectively in professional settings.

Syllabus

Advanced Bayesian Inference

Welcome to Advanced Bayesian Methods and Applications! In this module, we will see an alternative to MCMC that is able to scale to large datasets, namely, Variational Inference (VI). VI transforms the sampling problem to an optimization one and trades off accuracy for speed. We will also learn how to implement these approaches and when we should prefer VI over MCMC.

Bayesian Decision Theory & Prediction

In this module, we will learn how to use the uncertainty quantified by Bayesian analysis and loss functions to make decisions in a principled way. We will also look at multi-objective decisions, where we have to balance several - possibly conflicting - objectives.

Bayesian Non-Parametric Methods

In this module, we will explore the world of non-parametric Bayesian models. These models provide a lot of flexibility and allow the model complexity to grow with the data. We will see how Gaussian Process Regression and Dirichlet processes work with applications on function estimation and clustering, respectively. We will finally see that this flexibility comes with an important cost - computational complexity - which might hinder the applicability of these methods on large-scale problems/data.

Probabilistic Programming and Bayesian Workflow

In this module, we are going to put together pieces that we have seen throughout the course and all together form what we call the Bayesian workflow. We will define probabilistic programming and focus on the use of PyMC for building Bayesian models. We will see an end-to-end example of Bayesian inference that incorporates all the necessary steps of the workflow.

Bayesian Methods in Sports Analytics and Medicine

In this module, we are going to look at specific applications of Bayesian modeling and inference in two fast-evolving fields, sports analytics and medical informatics. We are going to see how we can use Bayesian models to obtain team strengths, including the uncertainty around this estimate. We will also see 2 applications in medical informatics; one for disease progression and one for predicting treatment effect.

Course Wrap-Up

In this module, we will see a full summary of the course starting from Bayesian thinking and moving to Bayesian inference. We will then make a stop on one of the most important Bayesian modeling frameworks, namely, hierarchical models, and we will finally wrap up with the ultimate task we have in the real world, i.e., decision making.