Data Analysis and Monte Carlo Methods
Module PH2100
Basic Information
PH2100 is a semester module in English language at Master’s level which is offered in summer semester.
This module description is valid to SS 2015.
If not stated otherwise for export to a non-physics program the student workload is given in the following table.
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 150 h | 75 h | 5 CP |
Responsible coordinator of the module PH2100 is Allen C. Caldwell.
Content, Learning Outcome and Preconditions
Content
(1) Probability Theory (Logical foundations, Bayes Theorem, data analysis as learning rule)
(2) The basic distributions (Binomial, Poisson, Gauss, etc including derivations, central limit theorem, ...)
(3) Formulation of data analysis with detailed examples
(4) Likelihood methods, chi-squared minimization (discussion of di erent techniques and their interrelationship)
(5) hypothesis testing, goodness-of- fit (Bayes formulation, frequentist formulation, test statistics and p-values, comparison of approaches and discussion)
(6) introduction to random numbers (generation of uniform rns, generation of rns according to arbitrary distribution)
(7) integration and optimization with random numbers (hit-or-miss, sample mean, importance sampling, simulated annealing)
(8) Markov chains and Markov Chain Monte Carlo (De nitions & derivations of MCMC, random walks, ergodicity and detailed balance)
(9) Metropolis, Metropolis-Hastings and other Monte Carlo methods for mapping probability densities
These topics will be introduced in the context of examples drawn from physics. Example data analyses:
(1) detector efficiency analysis
(2) radioactive decay time constant extraction in samples including background
(3) Supernova 1987 time arrival spectrum - how strong is the evidence ?
(4) neutrinoless double beta decay - sensitivity analysis
(5) energy spectrum in particle physics - extracting the underlying energy spectrum from an observed spectrum
(6) signal discovery conditions - analyzing a data set with diff erent background and signal assumptions and determining if a signal is present
Examples with random numbers:
(1) generating random numbers according to many di fferent distributions - special/efficient techniques
(2) Generating random background events starting from observed data
(3) simulation of Ehrenfest model for diff usion through a membrane
(4) simulation of Ising model
(5) solution of traveling salesman problem via simulated annealing
Learning Outcome
learn techniques at a level that the student can apply them to research problems
Preconditions
ability to program algorithms
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VU | 4 | Data Analysis and Monte Carlo Methods | Caldwell, A. |
Mon, 16:00–18:00, PH II 227 and dates in groups |
eLearning |
Learning and Teaching Methods
lecture, beamer presentation, board work
Media
accompanying internet site