Goals

The primary goal of the school is to train astronomers to the use of modern statistical techniques, specifically parameter estimation and model selection. The INTENSIVE course is characterized by extended laboratory sessions (i.e. individual work at the computer), taking about two third of the school attendance. Attendance to the course has pre-requirements specified HERE.

Program

1) Probability axioms. Computation of the posterior: analytical vs numerical sampling. Upper limits. Initial discussion on the role of the prior. Importance of checking numerical convergence. A glimpse on sensitivity analysis.
2) Single parameters models. Combining information coming from multiple data. The prior (and the Malmquist-like effect). Prior sensitivity. Two-parameters models. Joint probability contours. Comparison of the performances of state-of-the-art methods to measure a dispersion.
3) Introduction to regression. Comparison of regression fitters. Regressions (of increasing difficulty): non-linear regression with non-gaussian errors of different sizes (but no error on predictor and no intrinsic scatter). Allowing systematics (intrinsic scatter). Allowing errors on x. Regressions with two (or more) predictors. A glimpse on other important issues such as mixture of regressions, non-random data collection, model checking.
4) Introduction to Bayesian model comparison. Automatic implementation of Occam's razor. The three levels of inference. The Bayesian evidence: Meaning and interpretation. Dependency on the choice of prior.
5) Computation of the evidence: are physical constants variable?

Main Instructor

Stefano Andreon
The lecturer in the last few years has taught at over 15 advanced courses and postgraduate schools in 7 countries on topics of Bayesian inference. He is a respected author of textbooks on the school subject, Astrostatistics: Bayesian Methods in Cosmology Astrostatistical Challenges for the New Astronomy. Bayesian methods for the physical sciences. Learning from examples in astronomy and physics.

Additional Instructor

Fabio Castagna
Fabio Castagna lectured part of this course, and advised the laboratory sessions, during past editions of this School. He has a degree in Statistics and currently is a PhD student in Data Science.

The capacity is limited to 20 participants (first come first served basis). The school is open to PhD students in physics, astrophysics and astronomy (they should register by July 1st). Participants to the school are requested to install a few software packages and to write some reading/plotting routines as detailed HERE prior to the beginning of the school. Failing to do so will significantly impair the learning outcomes.

PAYMENT DETAILS

The registration fee is 20 EUR and for that you will also receive a 60 EUR statistical book. To secure a place, partecipants are required to pay the registration fee using the Museum ticket system (REGISTRATION CLOSED).

The school will be held in Cupola Fiore of the INAF-Brera Observatory, located in via Brera, 28 in the center of Milano. It will start on monday 16 October 2023 at 14:00 and end on friday 20 October at 12:00. See how to reach us.

The school is organized by S. Andreon (INAF-OA Brera). LOC: S. Andreon, I. Arosio, C. Bernasconi, M. Carpino, C. Casellato, F. Castagna, M. Giuliani, M. La Bianca, F. Loiacono, A. Mandrino, R. Moncalvi, M. Santoro, and G. Trinchieri.