The Swiss engineering master's degree

One of the most used (statistical) models for inferential data analysis is the linear regression model. But it is restricted to a Gaussian distributed response and a linear function for linking the linear combination of predictors with the expected response. Generalized Linear and Additive Models (GLM, GAM) allow us to relax some of these restrictions by specifying a more general set of response distributions and non-linear link functions. Hence we can analyse a wider variety of real world phenomenon such as counts, binary outcomes proportions and amounts (i.e. non-negative real-valued data). The aim of this modelling approach is to better understand the response outcome induced by the predictors based on the available data, allowing for better and more informed interpretation of the phenomenon. The first part of this course will provide an overview over the GLM/GAM approach and will detail many benefits and a few pitfalls.

The second part of this course covers the very popular and growing field of Bayesian statistics. We start with the fundamental principles of a Bayesian approach to the analysis of data that allows for a better accounting of uncertainty and more explicit statements of assumptions. We illustrate the basic mathematical framework as well as explanations of philosophy and interpretation. We set up and discuss introducing examples and extend them to more challenging modelling approaches, where we assess the outcome of a parameter in the face of uncertainty of other parameters. Completion of this part will give you an understanding and the ability to perform basic data analyses doing the Bayesian way.

Compétences préalables

• Basic calculus and linear algebra
• Basic knowledge in probability, statistical inference and regression analysis on the level of Devore, Farnum and Doi, “Applied Statistics for Engineers and Scientists”, 2014 Cengage Learning.
• User knowledge of R, MATLAB, Python or any other statistical software.

Objectifs d'apprentissage

• The students are able to analyse data by Generalized Linear and Additive Models (GLM and GAM) and understand the benefits that these model approaches offer for the analysis of normally and non-normally distributed response variables.
• They also perceive the difference between a frequentist and a Bayesian modelling approach.
• The students acquire a comprehensive overview how the open source statistical environment R is used and are able to perform a data analysis applying the techniques introduced in the course on real data sets.

Catégorie de module

First Part (8 weeks):

• Review of the concepts of multiple linear regression analysis with respect to inference, prediction, model evaluation and variable selection. Introducing some advanced topics in linear regression modelling. (3 weeks)
• Extending the linear regression model to generalized linear and additive models including logistic, Poisson, and Gamma regression. Revise inference, evaluation and variable selection for such models. (5 weeks)

Second Part (6 weeks):

• Concepts of Bayesian statistics. Set up and make inference in a Bayesian model with specifying suitable prior distributions. (2 weeks)
• Making inference in a Bayesian framework by simulating from the model directly, via an exact approach and by applying MCMC-techniques, e.g. the Metropolis–Hastings sampling algorithm. (4 weeks)

The contents listed are illustrated with used cases from the industrial and scientific fields. The practical work is done with the open source statistical analysis environment R.

Méthodes d'enseignement et d'apprentissage

Classroom teaching and practical work on computer with the statistical analysis environment R.

Bibliographie

Slides and lecture notes will be available in addition to recommended book chapters.