ECTS
5 credits
Component
Faculty of Science
Description
This UE will enable :
Manipulate the main results of probability from a practical point of view. Reinforce understanding of random phenomena with numerical illustrations. Introduce students to Monte-Carlo simulation methods for numerically solving integration problems or calculating the probability of complex events. Complete knowledge of the main laws and their properties, with a view to applications to inferential statistics and statistical tests covered in the Master's program.
Objectives
This course follows on from the Probability Theory course and will build on the results seen in that course. It will enable you to complete your knowledge of the theory and practice of randomness, so that you can take up a Master's degree in Probability and/or Statistics. It will cover the following points
Part I: Generating the hazard
- pseudo-random generators
- random variable simulations: inverse distribution function method, rejection method, other laws (Box-Muller method for simulating a normal law, mixtures, simulation of a Poisson random variable from the sum of independent exponential variables)
- numerical illustrations the main results of the probability course: law of large numbers, Moivre-Laplace theorem.
Part II: Monte Carlo method
- Monte Carlo method for approximate integral calculation and variance reduction: antithetic variables, control variables, preferential sampling. Application to the simulation of rare events.
Part III: Supplements
- Gaussian vectors and link with the usual laws of inferential statistics (student, chi2) application to the construction of confidence intervals.
- simple random walks, problem of maximizing the expectation of a cost function in financial math.
Practical work to implement numerical methods will be carried out using R software.
Necessary prerequisites
Analysis and probability courses in L1, L2 and L3, in particular :
- HAX506X Probability Theory
Recommended prerequisites :
Basic programming in R
Further information
Hourly volumes :
CM: 18
TD : 15
TP: 12
Land: -