Hauptseminar WS 13/14: Monte-Carlo Methods

Information

General references

Topics and dates

Here you can find the listing and schedule of the topics we distributed in the first week. I have added a few bullet points for each topic to give an idea of the content I had in mind. Also, I have indicated ideas for the simple example programs. Please use these only as suggestions and if you have other ideas feel free to bring them up!

21.10. Frank Siegert:
Applications of Monte-Carlo methods in particle physics

28.10. David Meisel:
Random numbers

  • Classification: random vs. pseudo-random vs. quasi-random
  • Criteria for pseudo-random numbers
  • Algorithms
  • Example program: Implementation of a few algorithms and test of their properties, comparison to built-in random number generators

4.11. Max Hils:
Without Monte-Carlo methods: integration by numerical quadrature

  • Classification of algorithms
  • Error estimate and its scaling with the number of dimensions
  • Example program: Implement a few algorithms and compare their results for an analytically known 1D integral with the expected error estimates with fixed number of evaluations
  • Reference: Computational Physics http://www.comp-phys.tu-dresden.de/cp2013/

11.11. Lukas Schröder:
Monte-Carlo integration basics

  • Motivation and basic idea
  • Law of large numbers
  • Error estimate
  • Example program: Volume of a d-dimensional sphere in MC vs. (simple) classical integration. Estimate the (statistical) uncertainty of each result. Compare the runtime (= number of points N) necessary to reach a given accuracy target (e.g. 1%). Plot the scaling of the MC result with N for some fixed values of d. Discuss the scaling with d.

18.11. Fabian Heisse:
Improving Monte-Carlo integration: Stratified sampling

  • Motivation
  • Introduction to stratified sampling
  • Example program: Demonstrate improvement from stratified sampling for different suitably chosen (1D?) integrals

18.11. Christian Bartzsch:
Improving Monte-Carlo integration: Importance sampling

  • Motivation
  • Introduction to importance sampling
  • Example program: Demonstrate improvement from importance sampling for different suitably chosen (1D?) integrals

2.12. Jonas Golde:
Monte-Carlo integration: Adaptive methods (VEGAS)

9.12. Johannes Krause:
Monte-Carlo integration with the multi-channel method

  • Motivation and basic idea
  • Automatic adaptation of weights
  • Example program: Demonstrate improvement from a multi-channel for a suitably chosen integral (e.g. with double-peak structure)
  • Original reference: http://arxiv.org/abs/hep-ph/9405257

16.12. Philipp Horn:
Monte-Carlo sampling basics

  • Motivation
  • Inverse transform method
  • Hit-or-miss method
  • Example program: reproduce a given distribution function using inverse-transform and hit-or-miss including a comparison of different hit-or-miss input distributions

13.1. Martin Rehwald:
Particle collision phase space with the RAMBO algorithm

  • Phase space for n massless particles
  • RAMBO algorithm
  • Example program: Generate 10000 events for a 2->4 scattering of massless particles, with a fixed configuration of incoming momenta of p_{0,1}=(E, px, py, pz)=(1000, 0, 0, +-1000) and a uniform distribution of the outgoing momenta. Plot their distribution in the theta variable. (Display some of them in 3D. ?)
  • Original reference: http://dx.doi.org/10.1016/0010-4655(86)90119-0 (only from TUD)

20.1. Alexander Melzer:
Sampling generalised radioactive decay type distributions

  • Motivation
  • Parton branching probabilities and the analogy to radioactive decay
  • Veto algorithm
  • Example program: Simplified parton cascade: One splitting function, simplified splitting kernel
  • Reference: http://arxiv.org/abs/hep-ph/0603175 Section 4, in particular 4.2

27.1. Robert Wolff:
Monte-Carlo sampling with the Metropolis/Hastings algorithm