# Statistiques

## In brief

• Number of hours : 6 lectures of 1h45 + 4 exercice sessions of 1h45 + 3 practical sessions of 1h45
• Teaching language : french
• Teaching method : En présence
• Code : N5EN04B

## Objectives

Understand how to define a statistical model, to determine the main properties of estimators of the model parameters and finally to implement standard estimation methods (maximum likelihood, methods of moments, Bayesian estimators, confidence intervals)

Understand the concept of statistical test, how we can evaluate the performance of a test and how the Neyman Pearson theorem can be applied to binary hypothesis problems.

Understand the principles of goodness of fit tests (chi-square and Kolmogorov)

## Description

Estimation

- Statistical model and properties of estimators

- Cramér-Rao inequality

- Maximum likelihood

- Method of Moments

- Bayesian estimation

- Confidence intervals

Binary hypothesis tests

- Probability of false alarm, of detection and receiver operational characteristics (ROCs)

- Neyman Pearson theorem

- Chi-square and Kolmogorov tests

## Targeted skills

Principles of statistical estimation and of hypothesis testing

## Bibliography

Athanasios Papoulis and S. Unnikrishna Pillai, Probability, Random Variable and Stochastic Processes, McGraw Hill Higher Education, 4th edition, 2002.

## Needed prerequisite

Bases of probability theory, computation of integrals and series, bases of optimization theory and of linear algebra

### Session 1 ou session unique - Contrôle des connaissances

ModalitéNatureCoefficientRemarques
CC (contrôle continu) Oral/Ecrit80%Ex-Statistiques
CC (contrôle continu) Bureau d'Etudes20%BE-Statistiques

### Session 2 - Contrôle des connaissances

ModalitéNatureCoefficientRemarques
CC (contrôle continu) Oral/Ecrit80%Ex-Statistiques
CC (contrôle continu) Bureau d'Etudes20%BE-Statistiques

## Contact(s)

### TOURNERET Jean-yves

Phone : 2224

Email : Jean-Yves.Tourneret @ enseeiht.fr

### CHARVILLAT Vincent

Phone : 2171

Email : vincent.charvillat @ enseeiht.fr

TOURNERET JEAN-YVES

## Places

• Toulouse

### Contact

The National Institute of Electrical engineering, Electronics, Computer science,Fluid mechanics & Telecommunications and Networks

2, rue Charles Camichel - BP 7122
31071 Toulouse Cedex 7, France

+33 (0)5 34 32 20 00