Statistics of experimental data in physics

Duration

30h Th, 15h Pr

Number of credits

Lecturer

Yvik Swan

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

The course begins with an overview of key concepts of descriptive statistics: univariate (organization and representation of data, parameters of central tendency, shape parameters) and multivariate (parameters of central tendency and covariance matrix, linear regression); we also address the concepts of standard error and confidence intervals. The focus is mainly on the interpretation of the indicators obtained. The course continues with a relatively thorough description of the different notions of probability essential to a proper understanding of inferential statistics: probability measures (continuous, discrete, conditional) random vectors, distributions and densities,  expectations (both conditional and non-conditional), an overview of the most common probability  laws and the most important theorems of convergence. Subsequently we discuss the calculation of errors and the Monte-Carlo and then continue with mathematical statistics : point estimation (method of moments, M-estimators, maximum likelihood, evaluation), interval estimation (CI for mean, variance, proportion ...) hypothesis testing (general and tests for mean and variance) and fitting. Most  illustrations are performed in R statistical software. (freely available via http://cran.r-project.org/) 
 
 

Learning outcomes of the learning unit

At the end of the course, students will be able to calculate and interpret the traditional indicators (both from the practical and theoretical standpoint)  obtained during an empirical study of a data set.  The student will understand the basic concepts of probability and be able to perform any basic calculation of  risk. The student will know (both from the practical and theoretical standpoint) what probabilistic model is appropriate under what circumstances. The student will understand the basic principles of the point estimation and interval estimation, and he will understand the basic principles of a statistical test protocol. The student will know and be able to apply the classical parametric tests (adjustment, orientation, dispersion, ...), master the basics of regression, and will be able to study the propagation of errors. Finally the student will be able to set up a Monte Carlo protocol.

Prerequisite knowledge and skills

A good understanding of calculus is required. 

Planned learning activities and teaching methods

Ex cathedra teaching and exercise sessions

Mode of delivery (face-to-face ; distance-learning)

Recommended or required readings

Course notes as well as exercise sets are available through eCampous. 
Bibliography

• Albert A., Biostatistique, Les Editions de l'Université de Liège, 2005
• Bevington P.R. and Robinson D.K., Data Reduction and Error Analysis for the Physical Sciences, Third edition, McGraw-Hill, 2003
• Casella, George, and Roger L. Berger. Statistical inference. Vol. 2. Pacific Grove, CA : Duxbury, 2002.
• Dehon, Catherine, Jean-Jacques Droesbeke, and Catherine Vermandele. Eléments de statistique : 5e edition revue et augmentée.  2008.
• Dehon, C., Probabilités et inférence statistique, Notes de cours de l'Université libre de Bruxelles, 2011
• Haesbroeck G., Probabilités et Statistique mathématique, Note de cours de l'Université de Liège, 2004
• Haesbroeck G., Statistique descriptive et notions de probabilité, Notes de cours de l'Université de Liège, 2013
• Ruwet, C., Statistique des données expérimentales de la physique, Notes de cours de l'Université de Liège, 2013

Assessment methods and criteria

The first and second session exams will contain theoretical questions (some of which are announced in class) and exercises inspired by those studied during the year. The theoretical and practical parts are separated: the first to be solved without notes, the second to be solved with the help of the student's own computer. 

Work placement(s)

Organizational remarks

Contacts

Yvik Swan Département de Mathématique, Grande Traverse, 12, Sart Tilman, B-4000 Liège +32 4 366 94 76 yswan at  ulg.ac.be 

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