Motivation

• Fabrizia Guglielmetti

Which way a coin tossed in air will fall may be completely determined by laws of physics. Prediction of the trajectory, in order to get the face of the coin when it is on the ground, depends on many parameters (e.g. angular momentum of rotation, force at the time of the toss, wind pressure at various instants during the rotation of the coin). Its modelling will require incorporating a random structure and its outcome is uncertain. Going beyond gambling, we often come across events whose outcome is uncertain and the evaluation of experimental data is quite complex. The uncertainty could be because of our inability to observe accurately all the inputs required to compute the outcome. It may be too expensive or even counterproductive to observe all the inputs. The uncertainty could be due to the current level of understanding of the phenomenon. Quantification of the uncertainty is one of the most obsessive problems in the evaluation of experimental data. After an introduction to probability theory, a summary of Bayesian and Frequentist principles is given. The material is supported with examples.

Bayesian methods, not only for astronomical images

• Fabrizia Guglielmetti

Astronomical images are frequently difficult to analyse because images consist of a diffuse background with superposed celestial objects and corrupted by effects due to instrumental complexity. Previous methods, e.g. sliding windows and wavelet based techniques, suffer from describing large variations in the background, detection of faint and extended sources and sources with complex morphologies. Large systematic errors in object photometry and loss of faint sources may occur with these techniques. In this talk, two forward methods (BSS and D3PO) capable to identify automatically point sources, diffuse emissions, also when on the same line of sight, are described. The BSS technique (Guglielmetti, F. et al. 2009) is based on Bayesian mixture models, while D3PO (Selig, M. & Ensslin, T. 2013) is based on Information Field Theory (http://www.mpa-garching.mpg.de/ift/). Both technique are applied on images at high frequencies (energies > 0.1 keV) of the electromagnetic spectrum. Noise dominates the signal especially at these frequencies.

The frontier of analysis methods for particle physics

• Kyle Cranmer

Kyle will review the current statistical techniques being used for new physics searches at the LHC. He will identify weak points and challenges of the current methods and the efforts underway to improve upon them.

Variational Bayes: a versatile workhorse

• Frederik Beaujean

Fred will provide a pedagogical introduction to the variational Bayes framework. While it is typically used for clustering, he will show a new algorithm to sample from and integrate multimodal functions that makes use of all the goodness of variational Bayes. This algorithm is of immediate use to many particle-physics analyses, particularly in B physics.