Monte Carlo Methods in Advanced Statistics Applications and Data Analysis

18 Nov 2013, 08:00 → 22 Nov 2013, 18:00 Europe/Berlin

MPI Munich

Allen Caldwell (Max Planck Institute), Frank Steffen (MPIM), Kai Schweda (GSI), Kevin Kroeninger (University of Goettingen), Ralf Ulrich (KIT), Thomas Schoerner-Sadenius (DESY)

This school - the first one commonly organised by the three Helmholtz Alliances Terascale, HAP and EMMI and the Max Planck IMPRS EPP School - addresses physicists from particle physics, astro-particle physics and hadrons & nuclei at all career levels. The programme comprises lectures and exercises on important Monte Carlo based statistics and data analysis methods.

Topics:
- Basics of statistics and probability, random numbers and the Monte Carlo method
- Bayesian reasoning
- Information field theory
- Markov chain Monte Carlos
- Sampling and clustering
- Population Monte Carlo
- Nested sampling

More information on the contents of the individual presentations and exercises can be found connected to the respective timetable entries.

Welcome Welcome.MCatMPI.pdf

Monday, 18 November

1 Registration

2 Basics 1: Basis of statistics, probability etc.

Speaker: Allen Caldwell (Max Planck Institute)

Slides MPPstatschool.pdf

12:30 Lunch break

3 Basics 2: Random numbers, distributions etc.

Speaker: Allen Caldwell (Max Planck Institute)

15:30 Coffee break

4 Basics 3: Logic, information and Bayesian reasoning (lecture)

Speaker: Dr Torsten Ensslin (MPA)

18:30 Welcome reception

Tuesday, 19 November

5 Basics 4: Information field theory - from data to images (lecture)

The problem of reconstrucing 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.

Speaker: Dr Torsten Ensslin (MPA)

Slides ift_crash_course.pdf

10:30 Coffee break

6 NIFTY: Numerical information field theory

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.

Speaker: Marco Selig (MPA Garching)

Slides nifty-tutorial.pdf

12:30 Lunch break

7 Bayesian mixture modelling

A method to solve the long-lasting problem of disentanglement of the background from the sources is given by Bayesian mixture modelling (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.

Speaker: Fabrizia Guglielmetti (MPE Garching)

Slides FGuglielmetti_MPP2013.pdf

15:45 Coffee break

8 Multivariate analysis

Speaker: Balazs Kegl (LAL, Orsay)

Paper main.pdf

Slides slides.pdf

Wednesday, 20 November

9 Markov chain Monte Carlo 1

Speaker: Remi Bardenet (Oxford)

Paper mcmcTutorialBardenet.pdf

Slides slides.pdf

10:30 Coffee break

10 Markov chain Monte Carlo 2

Speakers: Ralf Ulrich (KIT), Remi Bardenet (Oxford)

12:30 Lunch break

11 BAT - a complex Markov chain Monte Carlo application

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.

Speaker: Dr Kevin Kroeninger (University of Goettingen)

Slides slides_BAT_KK.pdf

16:00 Coffe break

12 The STAN package: Bayesian Inference based on Hamiltonian Monte Carlo

Speaker: Michael Betancourt

Literature literatureRec.pdf

Thursday, 21 November

13 Basic sampling methods, convergence, variance reduction - and connections to MC event generators

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.

Speaker: Stefan Gieseke (KIT)

Slides and exercises munich13.pdf

10:30 Coffee break

14 Exercises on MC sampling

Speaker: Allen Caldwell (Max Planck Institute)

Exercises Exercises.pdf

12:30 Lunch break

15 Nested sampling

Speaker: Udo v. Toussaint (IPP Garching)

16:00 Coffee break

16 Nested sampling using PyMultiNest

Speaker: Johannes Buchner (MPE Garching)

Slides PyMultiNest tutorial & slides

18:30 School dinner

Friday, 22 November

17 Population MC 1

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.

Speaker: Frederic Beaujean (MPI Munich)

Slides lecture.pdf

10:30 Coffee break

18 Population MC 2

Speaker: Frederic Beaujean (MPI Munich)

Slides

• clustering.pdf
• mcmc.pdf
• pmc.pdf

12:30 Lunch break

19 Q&A session