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. Model likelihood as predictive data probability. The three three levels of inference.
5) Comparison with Frequentist hypothesis testing and p-values. The Bayesian evidence: Meaning and interpretation. Asymptotic behaviour. Prior-free evidence bounds. Sensitivity analysis. Dependency on the choice of prior.
6) Computation of the evidence: Savage-Dickey Density ratio (SDDR); Laplace approximation; nested sampling and MultiNest implementation. Model complexity and Kullback-Leibler divergence. Bayesian Model Averaging and applications in cosmology.

Instructors

Stefano Andreon and Roberto Trotta
The lecturers in the last few years have taught at over 30 advanced courses and postgraduate schools on topics of Bayesian inference. They are respected authors 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.

The capacity is limited to 35 participants (first come first served basis). The school is open to PhD students in astronomy, who have priority (they should register by May 15th), and if space allows, to post-doc and researchers. Participants to the school are requested to install a few softwares 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 80 EUR and for that you will also receive an 85 EUR statistical book. From May 15th, registration is open to all of you having a background in astronomy or physics (subject to availability). Please check availability with Gabriella Ardizzoia (segreteria.cifs@hotmail.it) before register. To secure a place, partecipants are required to pay the registration fee by one of the following methods:
1) bank transfer - using the coordinates below Recipient name: CIFS (Consorzio Interuniversitario di Fisica Spaziale) Recipient bank: INTESA SAN PAOLO IBAN: IT71Q 03069 09217 10000 0460045 SWIFT code: BCITITMM
2) credit card - by filling this form and sending it by email to segreteria.cifs@hotmail.it. or via fax to the scientific secretariat: Gabriella Ardizzoia, Consorzio Interuniversitario per la Fisica Spaziale (CIFS), Fax number: +39 011 670 5883. Please specify in the registration notes any request you might have for the receipt in order to get refund from your home institute.
For the invoice please fill this form with either name, last name, fiscal code, full residence address, and institution, or name and full address of your institution.
The fee will be refunded to you should the limit of 35 entrants be already achieved by the time you register.

The school will be held in seminar room in Sala Strumenti of the INAF-Brera Observatory, located in via Brera, 28 in the center of Milano. It will start on monday 12 June 2017 at 14:00 and ends on friday 16 June at 12:00. See how to reach us.