Program (detailed contents):
– Simulation of random variables and vectors: pseudo-random numbers, simulation by the inversion method of the probability distribution function, by the acceptance-rejection method and by specific simulation methods.
-Classical Monte Carlo methods: implementation, variance reduction by different methods (control variate, importance sampling, antithetic variates method).
– Markov chain Monte Carlo methods: reminders on Markov chains, Markovian law of large numbers, Metropolis-Hastings algorithm.
– Application with the Python software
MCMC methods
Description
Objectifs
At the end of this module, the student will have understood and be able to explain (main concepts): The student will be able to:
- The fundamental principles of simulating random variables and vectors.
- The classical methods for variance reduction when approximating numerically integrals by means of the Monte Carlo method.
-The approximation of integrals by means of the Monte Carlo method using Markov chains.
- Generate a real random variable by the inversion method.
- Simulate a random vector by the acceptance-rejection method.
- Choose appropriate techniques for variance reduction (control variate, importance sampling, antithetic variates method).
- Use the Metropolis-Hastings algorithm generating a reversible ergodic Markov chain with prescribed stationary distribution.
Pré-requis
Probability and Statistics (2MIC Semester 4).
Probability and Data Analysis (3MIC Semester 5).
Complements of Probability (3MIC MA Semester 5).
Évaluation
L’évaluation des acquis d’apprentissage est réalisée en continu tout le long du semestre. En fonction des enseignements, elle peut prendre différentes formes : examen écrit, oral, compte-rendu, rapport écrit, évaluation par les pairs…
En bref
Crédits ECTS :
Nombre d’heures :
EN 1 Clic
Annuaire
ENT
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