When observing data, the key question is: What I can learn from the observation? Bayesian inference treats all parameters of the model as random variables. The main task is to update their distribution as new data is observed. Hence, quantifying uncertainty of the parameter estimation is always part of the task. In this course we will introduce the basic theoretical concepts of Bayesian Statistics and Bayesian inference. We discuss the computational techniques and their implementations, different types of models as well as model selection procedures. We will exercise on the existing datasets use the PyMC3 framework for practicals.

The main topics are:

• Bayes theorem
• Prior and Posterior distributions
• Computational challenges and techniques: MCMC, variational approaches
• Models: Mixture Models, Bayesian Neural Networks, Variational Autoencoder, Normalizing Flows
• PyMC3 framework for Bayesian computation
• Running Bayesian models on a Supercomputer