LFU:online

Department of Astro- and Particle Physics Department of Astro- and Particle Physics

Stefano Andreon, PhD Stefano Andreon, PhD

706122

Bayesian Methods for the Physical Sciences

PR 1

1,5

Block

every 2nd year

English

Course Syllabus:

•

Probability axioms. Computation of the posterior: analytical vs numerical sampling.

Upper limits. Initial discussion on the role of the prior. Importance of checking numerical convergence. A glimpse on sensitivity analysis.

•

Single parameters models. Combining information coming from multiple data. The prior

(and the Malmquist-like effect). Prior sensitivity. Two-parameters models. Joint probability contours. Comparison of the performances of state-of-the-art methods to measure a dispersion.

•

Introduction to regression. Comparison of regression fitters. Regressions (of increasing difficulty): non-linear regression with non-gaussian errors of different sizes (but no er roron predictor and no intrinsic scatter). Allowing systematics (intrinsic scatter). Allowing errors on x. Regressions with two (or more) predictors. A glimpse on other important issues such as mixture of regressions, non-random data collection, model checking.

Course Syllabus:

•

Probability axioms. Computation of the posterior: analytical vs numerical sampling.

Upper limits. Initial discussion on the role of the prior. Importance of checking numerical convergence. A glimpse on sensitivity analysis.

•

Single parameters models. Combining information coming from multiple data. The prior

(and the Malmquist-like effect). Prior sensitivity. Two-parameters models. Joint probability contours. Comparison of the performances of state-of-the-art methods to measure a dispersion.

•

Introduction to regression. Comparison of regression fitters. Regressions (of increasing difficulty): non-linear regression with non-gaussian errors of different sizes (but no er roron predictor and no intrinsic scatter). Allowing systematics (intrinsic scatter). Allowing errors on x. Regressions with two (or more) predictors. A glimpse on other important issues such as mixture of regressions, non-random data collection, model checking.

Attenders will hear the instructor for a tiny fraction of the time, and then spend most of their time solving by themselves (with the teacher help) problems of increasing (statistical) complexity, often using real data (to be downloaded during the course). This poses constraints on requirements, and demands that the attenders attend

all

 

lectures.

see dates