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# Data Analysis and Monte Carlo Methods

## Module PH2100

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### 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.

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 efficiency 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/efficient 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

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

no info

### Module Exam

#### Description of exams and course work

In a written exam the learning outcome is tested using comprehension questions and sample problems.

#### Exam Repetition

The exam may be repeated at the end of the semester.

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