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