50th Heidelberg Physics Graduate Days

Cosmology is a rewarding subject to study for many reasons, one of which is that, with some caveats, we can make robust predictions from theory, and as a result the confrontation with experiment can be done very successfully with principled statistical techniques.  In these lectures, I will review the standard cosmological model and its successes and tensions, and then show how recent advances in analysis techniques, based on forward-modelling the structure formation process, can lead to more precise and accurate inferences about the Universe.  There are two approaches, one based on Bayesian Hierarchical Modelling, and the other using simulation-based inference (SBI), with the latter using neural networks or analytic techniques to find maximally informative summary statistics. These techniques are quite general, and could easily be developed for, and applied to, other areas of science, provided that a good theoretical model of the data exists.