An Introduction to Bayesian Statistics

The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. For a long time, its practical applicability was limited due to the lack of efficient estimation algorithms and general computing power. However, both have changed in the past few decades. Nowadays, Bayesian statistics (also known as probabilistic machine learning) is highly relevant in almost all quantitative sciences. When using Bayesian methods, analysts benefit from the ability to express and fit highly complex models, incorporate prior information when available, naturally obtain uncertainties estimates, and easily propagate those uncertainties to push-forward quantities such as (posterior) predictions. In this talk, I will give a brief introduction to Bayesian statistics, highlight its advantages and disadvantages and provide a look into the future of Bayesian statistics.