Curs DAM: An introduction to Bayesian Statistics through Astronomical Applications

Professor: Dr. Cecilia Mateu , CIDA, Venezuela

Dates: 5 de novembre (9:00-10:30), 6 de novembre (9:00 – 12:30)

Lloc: Seminari DAM

Obert als estudiants del màster i del doctorat i als membres del DAM

Contacte:  cesca @ am.ub.es

Programa:

Lecture 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).
Lecture 2
Nuisance parameters and Marginalization
Example: An Astrophysical application of the Coin Example
Coordinate Transformations. Example: Derivation of the ‘Sum in Quadrature’ rule.
Parallax example (negative measurements of the parallax, effect of positive definite prior for the distance).
Lecture 3
Probability distributions: example applications. Fitting a density model to data (Poisson), the IMF example (Pareto distribution).
Lecture 4
Many parameter problems: Importance sampling and Markov Chain Monte Carlo. A familiar example using MCMC (the astrophysical coin example). Topics: ABC - Approximate Bayesian Computation. Examples.
The course includes hands-on exercises from specific software packages in Python.