ICCUB Curso: "An introduction to Bayesian Statistics through Astronomical Applications"

Teacher: Dr. Cecilia Mateu (CIDA, Venezuela)

Dates: 24-27 October

Place:

  • 24th, 25th, 26th from 17:40 to 19:00 October, Room V12M (first floor)
  • 27 october, from 14:30 to 16:00, V724 Seminar room, 7th floor

Open to all master and predoc students

Contact: cesca@fqa.ub.edu

The goal of this course is to provide a first contact with Bayesian Inference to undergraduate and masters students. We will introduce basic probability concepts emphasizing the interpretation of probability in the Bayesian framework. We will use simple astronomical applications to illustrate applications of different probablity distributions, the use of nuisance parameters and marginalization, computation of confidence intervals, coordinate transformations and we will end with a short practical introduction to Markov Chain Monte Carlo sampling.

1)   The concept of probability in Bayesian Statistics. The Sum and Product Rules. Bayes’s Theorem. Example: Least Squares Minimization - Chi2. The Coin Example (the effect of sample size and varying priors).

2)    Nuisance parameters and Marginalization. Example: An Astrophysical application of the Coin Example. Confidence Intervals. Coordinate Transformations. Examples: Derivation of the ‘Sum in Quadrature’ rule, computation of confidence intervals in N-dimensions.

3)     Probability distributions: example applications. Fitting a density model to data (Poisson), inferring the  total luminosity of a population given the  observed number of RR Lyrae stars (Poisson + noise + transformations).

4)    Many parameter problems: Importance sampling and Markov Chain Monte Carlo. A familiar example using MCMC (the astrophysical coin example).