DescriptionStatistical methods provide tools for dealing with uncertainty and learning from information. There are several fundamentally different frameworks of statistics, including frequentist theories and Bayesian methods. However, most of these cannot deal satisfactorily with surprising data, so observations that had been deemed to be extremely unlikely, up to the point that an assumed model would deem them to be impossible. What can one do in such cases? Within this project, a range of topics can be studied in detail. For example, the theory of imprecise probability, which generalizes classical probability theory by assigning a set of probabilities instead of a single one to each event of interest, enables surprising data to be taken into account in a generalized Bayes setting - this is referred to as `prior-data conflict'. It is of interest to consider the effect of such surprising data on statistical inferences and related decisions. In risk analysis, surprising observations have often been referred to as `black swans'; it is interesting to study such scenarios from perspectives of statistical methods and decision theory. A `formal Bayesian theory of surprise' has also been suggested, where `surprise' is based on the difference between corresponding prior and posterior probabilities. Critical investigation of this theory is also of interest, and can be linked to the two topics suggested above.PrerequisitesBayesian Statistics III is required, it is an advantage if you have also done Decision Theory III, particularly if you wish to focus on risk analysis.Further informationImprecise probability methods to reflect prior-data conflict have only recently been developed, mainly by Dr Gero Walter. It is best to discuss options with him, please contact him by email: gero.walter@durham.ac.uk. About the `Black Swans', see wikipedia. A webpage about the `formal Bayesian theory of surprise' is available here.Please feel free to contact me - best by email |
email: Frank Coolen