Bayesian statistics for astronomers and physicists
7.5 credits cr.
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The course covers the fundamentals of probability theory, including Bayes’ theorem, and how these concepts can be used to do inference and analyze experimental data. It also covers the numerical techniques, such as Markov chain Monte Carlo (MCMC), necessary to apply Bayesian inference to practical research problems within astronomy and physics.
In this course you will learn to apply the fundamental laws of probability theory, in particular with regards to densities and marginalization, and will become familiar with the use of Bayes’s theorem for inference in both discrete and continuous settings. By working through examples in class you will learn to apply Bayes’s theorem to generic astronomy and physics data analysis tasks, such as parameter estimation and model comparison. Finally, you will implement/program Markov chain Monte Carlo (MCMC) techniques and/or use available software packages, such as the Metropolis algorithm or Gibbs sampling, as well learning how to critically assess the results of such methods.
This course can be taken as part of the Masters programme in Astronomy, and can also be taken by Astronomy and Physics PhD students. It is given during the day and is delivered in English.
The course is taught through a combination of online lecture recordings (approximately 10 hours in total) and in-person discussion/problem sessions. These will focus primarily on worked examples, including numerical sampling techniques (e.g., MCMC), with students developing their own numerical software on their laptop computers during the sessions.
The course will be assessed through two take-home assignments. The first, worth 30% of the final mark, will cover the theoretical aspects of the course; the second, worth 70% of the final mark, will additionally utilize the numerical methods covered in the second half of the course. Students will be able to work on this assignment during the “hands on” coding sessions.
ScheduleThe schedule will be available no later than one month before the start of the course. We do not recommend print-outs as changes can occur. At the start of the course, your department will advise where you can find your schedule during the course.
Note that the course literature can be changed up to two months before the start of the course.
Data Analysis: A Bayesian Tutorial (2nd edition), Sivia, D. (& Skilling, J.), Oxford University Press
Bayesian Logical Data Analysis for The Physical Sciences, Gregory, P., Cambridge University Press
Practical Bayesian Inference, Bailer-Jones, C., Cambridge University Press
Probability Theory: The Logic of Science, Jaynes, E. (& Bretthorst, L.), Cambridge University Press
Bayesian Data Analysis (3rd edition), Gelman, A., et al., Chapman & Hall
The academic advisor and student office can be contacted via firstname.lastname@example.org.