Monte Carlo Methods in Advanced Statistics Applications and Data Analysis

Description of contents

 
Tuesday, 09.00 – 10.30h   Torsten Ensslin

Title	Basics 4: Information field theory - from data to images (lecture)
Description	The problem of reconstructing an image or a function from data is generally ill-posed. The desired signal has an infinite number of degrees of freedom whereas the data is only providing a finite number of constraints. Additional statistical information and other knowledge has to be used to regularize the problem. Information field theory permits us to formulate signal inference problems rigorously using probabilistic language to combine data and knowledge. It helps us to exploit existing methods developed for field theories to derive optimal reconstruction algorithms. In this course, an introduction to the basic principles of information field theory will be given and illustrate by concrete examples from astrophysical applications.

 

Tuesday, 11.00 – 12.30h   Marco Selig

Title	NIFTY: Numerical information field theory
Description	This Tutorial introduces NIFTY, "Numerical Information Field Theory", which allows a user an abstract formulation and programming of SIGNAL inference AND IMAGE RECONSTRUCTION algorithms. NIFTY is a versatile Python library designed to enable the development of signal inference algorithms that operate regardless of the underlying spatial grid and its resolution. The Tutorial covers the simulation of mock data from Gaussian random processes and a Wiener filter reconstruction of the underlying signal field from this data set. Using NIFTY, this filter can be applied on a variety of spaces; e.g., point sets, n-dimensional regular grids, spherical spaces, their harmonic counterparts, and product spaces constructed as combinations of those.

 

Tuesday, 14.00 – 15.45h   Fabrizia Guglielmetti

Title	Bayesian mixture modelling
Description	A method to solve the long-lasting problem of disentanglement of the background from the sources is given by Bayesian mixture modeling (Guglielmetti F., et al., 2009, MNRAS, 396,165). The technique employs a joint estimate of the background and detection of the sources in astronomical images.   Bayesian probability theory is applied to gain insight into the coexistence of background and sources through a probabilistic two-component mixture model. Uncertainties of the background and source signals are consistently provided. Background variations are properly modelled and sources are detected independent of their shape. No background subtraction is needed for the detection of sources. Poisson statistics is rigorously applied throughout the whole algorithm.   The technique is general and applicable to count detectors.   Practical demonstrations of the method will be given through simulated data sets and data observed in the X-ray part of the electromagnetic spectrum from ROSAT and Chandra satellites.

 

Wednesday, 14.00 – 16.00h   Kevin Kroeninger

Title	BAT - a complex Markov chain Monte Carlo application
Description	BAT - a complex Markov chain Monte Carlo application   The tutorial will give an introduction to the Bayesian Analysis Toolkit (BAT), a C++ tool for Bayesian inference. The software is based on algorithms for sampling, optimization and integration where the key algorithm is Markov Chain Monte Carlo. Interfaces to existing software tools exists, e.g., the ROOT implementation of Minuit, and the Cuba library. A simple physics example will be discussed and formulated as a statistical model in BAT. The first steps will include the calculation of marginal distributions and uncertainty propagation. The example will also be used to explain the basic functionalities of BAT.

 
 
Thursday, 09.00 – 10.30h   Stefan Gieseke

Title	Basic sampling methods, convergence, variance reduction - and connections to MC event generators
Description	We consider Monte Carlo methods specific to the use in Monte Carlo event generators.  After an introduction to Monte Carlo sampling or integration we will discuss some methods of variance reduction with phase space integration as application in mind.  Finally we briefly discuss Multi Channel integration as the key to the integration of multi body final state matrix element.

 
 
Friday, 09.00 – 10.30h   Fréderic Beaujean

Title	Population MC 1
Description	Adaptive importance sampling, or population Monte Carlo (PMC), is a powerful technique to sample from and integrate over complicated distributions that may include degeneracies and multiple modes in up to roughly 40 dimensions.  PMC is best for tough problems as the costly evaluation of the target distribution can be massively parallelized.   Based on a simplified global fit for new physics, the individual parts of the algorithm ranging from the initialization over proposal-function updates to the final results are presented step by step in a hands-on and visual fashion. Only basic knowledge of C++ is required in order to modify the given source-code examples for a more rewarding learning experience.