Bayesian learning

The course provides an introduction to Bayesian learning, prediction and decision making with a focus on modern applications in statistics and machine learning. The main ideas behind Bayesian inference are first presented in a number of simpler models, and then gradually move on to the analysis of more complex models using modern simulation and approximation methods. Bayesian inference uses Bayes' theorem to combine data information with other sources of knowledge in a probabilistic approach. This so-called a priori information can consist of expert knowledge, previous studies or other data sources, but also more subjective information about the degree of softness in the relationship between predictor variables and a target variable in a flexible prediction model. A Bayesian approach provides a quantification of uncertainty that can be used for decision-making under uncertainty. The course contains several mathematical exercises and computer labs to teach the application of Bayesian methods for: regression, classification, regularization, prediction, optimal decisions, variable and model choices. Simulation methods such as the Markov chain Monte Carlo and the Hamiltonian Monte Carlo are an important part of the course; optimization-based approximation methods such as variational inference are also addressed.