Coursebooks 2017-2018

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Stochastic simulations

MATH-414

Lecturer(s) :

Nobile Fabio

Language:

English

Summary

The student who follows this course will get acquainted with computational tools used to analyze systems with uncertainty arising in engineering, physics, chemistry, and economics. Focus will be on sampling methods as Monte Carlo, quasi Monte Carlo, Markov Chain Monte Carlo.

Content

- Random variable generation
- Simulation of random processes
- Monte Carlo method; output analysis
- Variance reduction techniques (antithetic variables, control variables, importance sampling, ...)
- Rare events simulations
- Quasi Monte Carlo methods
- Markov Chain Monte Carlo methods (Metropolis-Hasting, Gibbs sampler)
- Stochastic optimization (stochastic approximation, simulated annealing)

 

Other topics that may be addressed if time allows:
- Estimation of derivatives
- Filtering problem; particle filters
- Simulation of Gaussian random fields and Kriging.

Keywords

Simulation of random variables and processes; Monte Carlo; Quasi Monte Carlo; Markov Chain Monte Carlo

Learning Prerequisites

Required courses

basic Probability and Statistics; Numerical Analysis;

Recommended courses

Applied Stochastic Processes (or equivalent)

Important concepts to start the course

Knowledge of basic courses in mathematics, probability, statistics and numerical analysis. Some experience of computer programming is assumed.

Learning Outcomes

By the end of the course, the student must be able to:

Transversal skills

Teaching methods

course ex-cathedra + exercise sessions and computer labs

Expected student activities

Active participation to the course and practical sessions

Assessment methods

The final exam may require the use of a computer.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Office hours Yes
Assistants Yes
Forum No

Resources

Virtual desktop infrastructure (VDI)

Yes

Bibliography

S. Asmussen and P. Glynn, Stochastic Simulation: Algorithms and Analysis. Springer-Verlag, 2007
G. Robert and G. Casella, Monte Carlo statistical methods, Springer 2004
D. Kroese, T. Taimre and Z. Botev, Handbook of Monte Carlo Methods, Wiley 2011
G. Robert and G. Casella, Introducing Monte Carlo methods with R. Springer 2010

Moodle Link

In the programs

Reference week

 MoTuWeThFr
8-9  CM013  
9-10    
10-11  CO4
CO6
  
11-12    
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German