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.

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.

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.

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.

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.

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.