ASTROSTATISTICS

Students are expected to develop a solid understanding of the underlying theory and gain hands-on experience in interpreting observational and experimental astrophysical data. The course will provide a foundation in Bayesian inference and demonstrate how it is applied in modern data analysis, with numerous examples drawn from astrophysics.

Basics of classical physics, math, Fourier analysis, and a basic familiarity with coding in Python/C.  It is advisable, though not required, to have attended a course in Cosmology.

• Introduction to probability theory
• Bayes' equation and inference
• Methods for computing the posterior, including Monte Carlo techniques
• Compression
• Regression
• Basics of Neural Networks and their application to the inverse problem
• Simulation based inference

All lecture notes and other materials will be provided in class.

Each student will be assigned an exercise or a small research project and the results will be the starting point for the oral exam discussion. Its aim is to probe the level of comprehension of the central concepts, their applications, and the link to observations.

• What is a prior in Bayesian inference? When are priors important and when are they not? How should they be chosen and what should be done if there is no obvious choice? Be explicit with examples/figures.
• Describe the steps involved in performing principal component analysis. Be as quantitative as possible.