To develop statistical and programming skills that will allow the students to perform their own measurements of relevant astrophysical quantities. Many of the measurements considered in the course will require the use of large databases ("big data science"; see for example the Gaia astrometric satellite). The first part of the course will focus on the statistical tools required for the various projects, with particular emphasis on Bayesian statistics. Students will also have the opportunity to learn the Python programming language. Most of the proposed measurements will be of astrophysical nature, but the skills developed during the course will also be useful for students with different interests and backgrounds
Expected learning outcomes
At the end of the course the student will be able to
1. Formulate a physical and statistical model of a well-posed astronomical problem.
2. Understand and be able to apply Bayesian inference statistical techniques.
3. Use data from the major astronomical archives and perform with them some preliminary analyses to improve the physical and statistical understanding of a system.
4. Know the basics of scientific programming in the Python language and be able to implement programs to perform Bayesian inference starting from simulated and real data.
5. Appreciate the importance of numerical stability and efficiency of algorithms, especially if applied to systeems with large data volumes.
Lesson period: Second semester
(In case of multiple editions, please check the period, as it may vary)
ntroduction to probability theory · Random variables, probability distributions · Meaning of probability: frequentist and Bayesian interpretation · Correlated random variables, moments, dependent variables · Bayes' theorem and its simplest interpretation · Bayesian inference · Maximum likelihood · Laplace's method · Simple clustering algorithms · Bayesian model comparison · Monte Carlo methods
Sample applications · Local star clusters from Gaia DR1 and 2 · Analysis of microlensing events from the OGLE database · Distance of the Large Magellanic Cloud from eclipsing binaries · Misurement of H0 from cefeids · Analysis of the kinematics of a spiral galaxy from integral field unit data · Analysis of a strong gravitational lens · Fundamental plane using the SLOAN Digital Sky Survey
Prerequisites for admission
No specific prerequisites are required in addition to those provided by the compulsory courses of the first two years of the three-year degree in Physics.
The course includes a series of lectures in which the necessary statistical bases are provided. Additionally, programming techniques in the Python language are also briefly introduced. Then, at the beginning of each experience, the astrophysical problem that is intended to be solved is briefly described: this way the students are able to carry out the analysis independently.
Reference text: David MacKay, "Information Theory, Inference, and Learning Algorithms", Cambridge University Press, 2003
For some of the problems addressed, a reading of some parts of
Peter Schneider, "Extragalactic Astronomy and Cosmology", Springer, 2006
can be of help.
Assessment methods and Criteria
During the lab hours, the students, divided into groups, will have to carry out the assigned task independently. The results obtained must then be presented by each group in a short report, which will be evaluated. The final evaluation will take into account the marks obtained by each student in the reports and the result of an oral exam (lasting approximately 45 minutes).