Statistical modeling and dynamic systems

The aim of this course is to introduce various modeling approaches, including scalar discrete dynamical systems and the generalized linear model in statistics (using R software for the "statistical modeling" part).

Prerequisites: linear algebra, analysis, optimization, probability, unidimensional and multidimensional descriptive statistics and inferential statistics (modules CO5SFMA0 and CO6SFMA0).

Theme 1: Statistical modeling (12h CM 16h TD - Lecturer: Jérôme Saracco)
Chapter 1: General introduction

What is statistics?
Course content and objectives

Chapter 2: Brief introduction to some linear models

Simple linear regression model
Multiple linear regression model
Analysis of variance model
Summary table

Chapter 3: Simple linear regression model

The model
Estimation of model parameters
Hypothesis testing and confidence interval for the slope parameter
Coefficient of determination
Prediction of a future value
Some useful supplements

Chapter 4 : Multiple linear regression model

The model
Estimation of model parameters
Geometric aspect of least squares
Case of the linear Gaussian model
Coefficient of determination
Hypothesis testing and confidence intervals for model coefficients
Prediction interval for a future value
Variable selection

Chapter 5 : Analysis of variance model (ANOVA)

One-factor analysis of variance
Relationship between one-factor analysis of variance and the linear Gaussian model
Two-factor analysis of variance and more than two factors
Some quick notions of analysis of covariance (ANCOVA)

The "Statistical Modeling" theme is subject to continuous assessment (in the form of an R project, coef. 2.5) and a written exam lasting 1h30 with authorized documents (coef. 5) at the end of the semester.
Theme 2: Scalar dynamic systems (4h CM 5h20 TD - Lecturer: Christophe Jauze)
Chapter 1: General presentation
Chapter 2: Reminders on numerical sequences
Chapter 3: Sequences defined by a recursive linear relationship
Chapter 4: Sequences defined by a non-linear function on two consecutive terms
Chapter 5: Generalization
The "Scalar dynamic systems" theme is subject to continuous assessment (in the form of a homework assignment, coef. 1) and a written exam lasting 1h30 without documents (coef. 2) during the semester.
Authorized documents (da) for exams on themes 1 and 2:
Only one double-sided A4 sheet of personal handwritten notes is authorized for exams (in sessions 1 and 2). Photocopies are not permitted. This document will be returned with the exam paper, and will be returned at the student's request after marking.
"Philosophy of TDs":
Theme 1: Statistical modeling

The aim of TDs is to understand the underlying stochastic models and associated methodologies, and to interpret estimated models (numerical and graphical outputs from R statistical software) in the context of real-life problems.

Theme 2: Scalar dynamical systems

Practical exercises focus on applications that may be related to problems in finance, demography, electronics, etc.

"Philosophy of practical exercises:
Theme 1: Statistical modeling

Statistical modeling concepts covered in lectures and practical exercises are implemented with R, using simulated and real data associated with a variety of problems (environment, biology, etc.).).

Theme 2: Scalar dynamic systems

There are no practical exercises for this theme.

"Project philosophy":
Theme 1: Statistical modeling

Engineering students are required to carry out a project in R as part of their continuous assessment (CC). The aim of the project is to apply the concepts of statistical modeling covered in class/DD/PT to real data and problems.

Theme 2: Scalar dynamic systems

There is no project as such, but students are required to do an individual homework assignment.

Applied mathematics