Probabilités et statistique

Summary

A first course in probability and statistics

Content

Motivation: random experiment; probability space; conditional probability; independence.

Random variables: basic notions; density and mass functions; examples; mean, variance,  correlation and covariance; joint distributions, conditional and marginal distributions; transformations.

Notions of convergence; laws of large numbers; central limit theorem; delta method; applications.

Descriptive statistics: basic graphs and statistics; notions of robustness.

Statistical inference: hypothesis testing; types of point estimator and their properties; confidence intervals; likelihood inference; simple examples. 

Learning Prerequisites

Required courses

Analyse I, II, Algèbre linéaire

Teaching methods

Ex cathedra lectures and exercise classes.

Assessment methods

Mid-term test, final exam

Supervision

Resources

Bibliography

- Dalang, R. C. et Conus, D. (2008). Introduction à la théorie des probabilités. PPUR: Lausanne. 

- Davison, A. C. (2003). Statistical Models. Cambridge University Press: Cambridge. Sections : 2.1, 2.2;  3.1, 3.2; 4.1-4.5; 7.3.1; 11.1.1, 11.2.1. 

- Morgenthaler, S. (2014). Introduction à la statistique, 4ème édition. PPUR: Lausanne. 

Random exercise generator
- Random exercise generator

R and RStudio
- R-project
- Comprehensive R Archive Network (CRAN)
- RStudio

Visualisations

- Confidence intervals
- Frequentist inference
- Seeing theory

- Statistics Tools for Internet and Classroom
- Web Pages that Perform Statistical Calculations

- Gallery of Data Visualization

- Visual Trumpery (talk by Alberto Cairo)

- NIST/SEMATECH e-Handbook of Statistical Methods

- Rice Virtual Lab in Statistics
- Virtual Laboratories in Probability and Statistics
- Statoo Consulting's Statistical Links
- Professor Risk
- The Joy of Stats
- History of Mathematics
- Statistics and Probability Encyclopedia
- Getstats
- Straight statistics
- Significance
- Why learn math?
- Jelly beans and multiple testing
- Machine Learning