Statistical Inference

The goal of this course is to provide the students with the tools to carry a procedure of statistical inference (as well in the Bayesian as in the frequentist paradigms), as soon as they are given a probabilistic model adequate to the situation encountered, plus the mathematical tools adapted to that model. Also, they will be able to understand the precise meaning of a statistical analysis carried by someone else, and to have a critical look at that analysis and its relevance.

Statistics is an absolutely essential tool to interpet correctly data that are impacted by some randomness.  This science is massively used in all the fields of engineering: you may use it either for analysis procedures, for decision taking, for process control, or for prediction of the future.  This course introduces, in a general framework, all the main methods of inferential statistics (in particular: estimation, hypothesis testing, confidence intervals), both in the purely inferential paradigm and in a predictive context.  Both the Bayesian and frequentist apporaches are being tackled.  All standard statistical procedures (e.g. Student, χ², Snedecor tests) can be understood thanks to the framework presented, as well as all standard procedures of data analysis (e.g. linear and logistic regressions, discriminant analysis, &c.).  However, the aim of the course is not to know these standard procedures: the goal is rather to understand, in full generality, the deep meaning of the concepts of statistics, so that one can carry out efficiently any method of statistical inference (whether it is standard or not), once being given the appropriate mathematical tools.  Another core aim is that, at the end of the course, the students get able to look critically at a given procedure of statistical inference (whether it was carried by themselves or by someone else), concerning both the relevance of the model used and the way the results are interpreted.

To understand the precise meaning of the methods of statistical inference, in particular the way that they depend on the underlying model, and also the difference in interpreting the Bayesian and the frequentist paradigms.

To give a relevant interpretation for the raw results yielded by a statistical analysis.  To draw the appropriate conclusion from these in an industrial context.

To be able to have a critical look at the choice of the statistical method used to analyze some data, resp. at the conclusions that were drawn from that analysis.  If needed, to challenge that method and/or these conclusions by using scientifically sound arguments.