# Elements of Statistical Modelling

## Presentation

• Nonparametric statistics: empirical distribution function, Kolmogorov test, normality tests
• Chi-square goodness-of-fit test, Chi-square independence test
• Linear models: estimation of the parameters, confidence intervals, prediction intervals, Fisher test for a sub-model, model selection and model validation.
• Generalized linear model: statistical inference, variable selection .

## Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

• The use of statistical tests for goodness-of-fit, independence, populations comparisons
• The characteristics of a linear model and a generalized linear model, and their use for statistical modelling

At the end of this module, the student should be able to:

• Use  nonparametric testing procedures  to compare two populations
• Build goodness-of-fit tests for a single distribution or a family of distributions
• Estimate the parameters in a linear model and a generalized linear model
• Use statistical tests to validate or invalidate hypotheses on these linear models.
• Solve a model selection problem
• Explain the principle of the experimental design
• Perform a complete statistical analysis on a real data set with a linear model or a generalized linear model

## Needed prerequisite

Probability and Statistics (I2MIMT31)

Statistics (I3MIMT15)

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...