Programming in R

This course is designed for first-year Master’s students in Mathematics to prepare them for computer programming. Programming refers to the comprehensive set of activities that enable the development of software programs. This process of writing programs is executed within a programming language. R is an open-source programming language dedicated to statistical analysis and data science.

Mathematical modelling

Compléments de Théorie de la Mesure

The course "Compléments de la théorie de la mesure" (Complements of Measure Theory) is a core graduate module offered in Semester 1 of the Master 1 in Probabilities, Statistics, and Applications program.  It carries 4 Credits, a Coefficient of 2, and consists of 42 hours of classroom instruction (1h30 lecture and 1h30 tutorial/TD per week) along with 58 hours of personal study.

Course Goal & Prerequisite

  • Objective: To master the formal, rigorous measure-theoretic framework necessary for modern probability theory and advanced stochastic analysis. 
  • Prerequisite: Introductory undergraduate Measure Theory (L3 level).

 

 

Inferential statistic

Statistical inference aims to draw conclusions about a population from a sample.
The course introduces the main concepts of point estimation and the properties of estimators.
It covers Maximum Likelihood Estimation and the Method of Moments.
Important properties include bias, variance, consistency, efficiency, sufficiency, and completeness.
Fisher information and the Cramér–Rao lower bound are also studied.
The course introduces confidence interval estimation for means, variances, and proportions.
Students learn how sample size affects the precision of an estimation.
The final part introduces statistical hypothesis testing and the Neyman–Pearson approach.
Type I and Type II errors, test power, critical regions, and parametric tests are discuss