The objective of this course is to show students how statistics is used in practice to answer a specific question, by introducing a series of important model-based approaches.

The students will learn to select and use appropriate statistical methodologies and acquire solid and practical skills by working-out examples on real-world data sets from various areas including medicine, genomics, ecology, and others.

All analyses will be conducted with the R software, possibly with interfacing to Python. No strong knwoledge neither of R nor Python programming is required (only basic scripting).

Course Evaluation: 2 individual homework assignements + a final exam/project

Course Language: French with all material in English

Website:  https://jchiquet.github.io/MAP566/

Syllabus

  1. Statistical tests (x1.5)

    • Two-populations comparison
    • Power analysis
    • Multiple Testing
  2. Regression models (x1.5)

    • Linear and Non Linear Regression models
    • Nonlinear regression models
    • Inference Diagnostic, Model comparison
  3. Mixed effects models (x2)

    • Linear mixed effects models
    • Nonlinear mixed effects models
  4. Mixture models and model-based clustering (x2)

    • Gaussian mixture models for data clustering
    • Stochastic Block Models for graph clustering
    • (Variational) EM algorithm
  5. Model-based Dimension Reduction (x2)

    • Multivariate Gaussian model
    • Probabilistic Gaussian PCA
    • Generalized mixed effect models

Langue du cours : Français

Credits ECTS : 4