Fiches de cours

Stochastic simulations

MATH-414

Enseignant(s) :

Nobile Fabio

Langue:

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

- Simulation of Gaussian random fields and Kriging.

- 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)

Other topics that may be addressed if time allows:
- Stochastic optimization (stochastic approximation, simulated annealing)
- Estimation of derivatives
- Filtering problem; particle filters

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

Miniproject + final written exam which 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
D. Kroese, T. Taimre and Z. Botev, Handbook of Monte Carlo Methods, Wiley 2011
G. Robert and G. Casella, Monte Carlo statistical methods, Springer 2004

Notes/Handbook

lecture notes available on the webpage

Moodle Link

Dans les plans d'études

  • Mathématiques - master, 2019-2020, Master semestre 1
    • Semestre
      Automne
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Stochastic simulations
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines
  • Mathématiques - master, 2019-2020, Master semestre 3
    • Semestre
      Automne
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Stochastic simulations
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines
  • Ingénierie mathématique, 2019-2020, Master semestre 1
    • Semestre
      Automne
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Stochastic simulations
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines
  • Ingénierie mathématique, 2019-2020, Master semestre 3
    • Semestre
      Automne
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Stochastic simulations
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines
  • Science et ingénierie computationnelles, 2019-2020, Master semestre 1
    • Semestre
      Automne
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Stochastic simulations
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines
  • Science et ingénierie computationnelles, 2019-2020, Master semestre 3
    • Semestre
      Automne
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Stochastic simulations
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines

Semaine de référence

LuMaMeJeVe
8-9 MAB1486
9-10
10-11 MAA331
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Cours
Exercice, TP
Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand