Bayesian Methods for the Physical Sciences

by Stefano Andreon

by Stefano Andreon

Program

Lecture 1)

Probability axioms. A first posterior computation, analytically and by numerical sampling. Upper limits. Intial discussion on the role of the prior. Importance of checking numerical convergence. A glimpse on sensitivity analysis.

Lecture 2)

Single parameters models. Combining information coming from more than one single datum. The prior (and the Malmquist-like effect). Prior sentitivity. A first two-parameters model. A first joint probability contour.

Lecture 3)

An additional two-parameter model (measuring the intrinsic scatter using these data). Comparison of the performances of state-of-the-art methods to measure a dispersion. Introduction to regression: a) pay attention to selection effects! b) avoid fishing expeditions c) prediction differs from parameter estimation (test it with this sample, generated with JAGS. Its CODAindex is here). Comparison of regression fitters: Bayes has a lower bias, fairer errors and less noisy errors.

Lecture 4)

Starting easy: non-linear regression with non-gaussian errors of different sizes (but no error on predictor and no intrinsic scatter). The data. Adding complexity: allowing systematics (intrinsic scatter), using these data. Elements of model selection (if time allows).

Lecture 5)

Adding more complexity (heteroscedastic errors on x, Magorrian relation), using these data. Regression with two (or more) predictors, using Planck data, to be done alone without any help. A glimpse on other important issues such as mixture of regressions, non-random data collection, model checking.

All the material is organized in this book, and also semi-randomly distributed in my papers.

The lectures are addressed to PhD students, post-doc and staff once registered.

To be admitted at the course you need in advance to fullfil some requirements (see my notes here), in particular a) to be able of drawing plots and make simple operations on numbers and vectors, and b) that JAGS runs on your computer. JAGS user manual is here. To test your reading of JAGS output use CODAchain1.txt and CODAindex.txt.