ECTS : 6
Lecturer in charge : Judith ROUSSEAU (https://dauphine.psl.eu/recherche/cvtheque/rousseau-judith)
Language of instruction : French
Teaching hours : 49
Course content:
- Statistics, the what and why
- Probabilistic models for statistics : parametric and non parametric models, identifiability
- Convergence theorems
- Likelihood function, statistical information, and likelihood inference
- Bayesian inference
Skills to be acquired:
This course is the first part of the two L3 statistics courses. It covers the fundamentals of parametric statistics, both from mathematical and methodological points of view, with some forays into computational statistics. The main theme is that modelling is an inherent part of the statistical practice, rather than an antecedent to the statistical step. Data may be a given, while models almost never are. This means one should keep a critical eye about models and develop critical tools to assess their adequation. Including, first and foremost, an assessment by simulation (Monte Carlo) methods. The course is entirely in English, except for the partial and final exams. Some practicals (TP) will be included, covering R language programming and applications to the bootstrap and Monte Carlo methodologies.
Mandatory prerequisites
A first course in (continuous) probability theory covering standard distributions, expectations, limit theorems, and conditional distributions
Recommended prerequisites
A first course in (continuous) probability theory covering standard distributions, expectations, limit theorems, and conditional distributions
Assessment:
Mid-term exam and final exam, potentially completed by quizzes and projects along the semester
Bibliography, recommended reading:
Casella and Berger (1989) Statistical Inference. Duxbury,
L. Wasserman : All about statistics.