Syllabus academic year 2007/2008

Higher education credits: 7,5. Grading scale: TH. Level: G2 (First level). Language of instruction: The course might be given in English. Compulsory for: RH3rh. Optional for: C4, C4sd, M3, N4, Pi4, Pi4mrk, V3. Course coordinator: Igor Rychlik,, Matematisk statistik. Recommended prerequisits: Basic course in Mathematical Statistics or Statistics. Assessment: Written exam and compulsory computer exercises. Home page:

The course presents notions and ideas from the foundations of a statistical treatment of risks. The emphasis lies on an understanding of the theory and methods presented. Hence the focus is put on applications within the field of risk and safety analysis.

Since in risks estimations one needs to combine information from different sources the Bayesian methods are frequently used in that area. Hence a reasonable proportion of the course is devoted to such approaches. In order to be able to analyse and predict frequencies of occurrences of hazardous scenarios, modern statistical tools, namely Poisson regression, analysis of deviance, extreme value theory and threshold methods are presented . The knowledge of such tools facilitates the understanding of the role of probability in risk analysis and proper use of outputs given by software packages.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

Judgement and approach
For a passing grade the student must

A review of elementary concepts in probability theory; Independence, conditional probabilities, random variables, probability distribution functions, expected value, variance, covariance.

Presentation and simple applications of Bayes' Theorem, Central Limit Theorem, Law of Large Numbers and Law of Small Numbers.

Classical statistical inference; maximum likelihood method, confidence interval, hypotheses testing (goodness of fit tests). Introduction to bootstrap and the delta method to construct confidence intervals.

Introduction to Bayesian statistics; predictive probabilities, conjugated priors, credibility intervals.

Intensities, Poisson modelling; estimation, Poisson regression.

Some concepts from safety and reliability analysis, failure intensities, safety indexes, characteristic values.

Estimation of quantiles using POT-method.

Introduction to extreme values statistics. Estimation of design events, e.g. strength of 100 years storm, and uncertainty analysis of the estimates.

Rychlik, I, & Rydén, J: Probability and Risk Analysis - An Introduction for Engineers. Springer 2006, ISBN 3-540-24223-6