Statistics and data sciences

At the end of this learning unit, the student is able to :

• Explore datasets of small and big sizes with few or many dimensions
• Infer features of a population from a sample using techniques of inference, estimation, confidence intervals and statistical tests.
• To connect the deductive approach from the probability theory to the statistical inductive approach, and to identify the probabilistic models used in statistical inference. 
• To translate the textual formulation of a problem of statistical inference into an accurate, statistical and mathematical formalism, while recognizing the adequate models and corresponding estimation methods.
• To solve an applied problem by following a logical approach based on a correct use of models and statistical inference.
• To use techniques of Monte-Carlo simulations, K-fold cross validation and bootstrapping in order to estimate models and validate results.
• To analyse multivariate data with fundamental methods of linear regressions, of principal component analysis and of classification/clustering.
• To use statistical tools to validate the conclusions from a model e.g. like the linear regression.
• To make the link between the mathematical objectives of a method of data mining and its practical purposes.