ICCUB COURSE – An introduction to Bayesian Statistics through Astronomical Application

2017-11-20

00:00

V12M (Facultat de Física)

ICCUB COURSE – An introduction to Bayesian Statistics through Astronomical Application

The goal of this course is to provide undergraduate and masters students a first contact with Bayesian Inference. 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.

Schedule: 20, 21 and 22 of November from 17:40 to 19:00

Programme:

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 Confidence Intervals. Coordinate Transformations.
Examples: Derivation of the ‘Sum in Quadrature’ rule,computation of confidence intervals in N-dimensions.

Lecture 3

Probability distributions: example applications. Fitting a density modelto data (Poisson).
Inference with many parameters: the “astrophysical coin” example using Markov Chain Monte Carlo.

The course is open to all pre- and postdoc students

Contact email: tantoja(a)fqa.ub.edu