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Reminder: There will be a Statistics seminar at UMIST on Wednesday 1st December. Details are given below. All those interested are welcome to attend. Wednesday 1st December, 4.00pm - 5.00pm Venue: UMIST, MSS/M12 Speaker: Professor Clive Anderson, The University of Sheffield. Title: The Largest Inclusions Within a Piece of Steel Abstract: The Largest Inclusions Within a Piece of Steel Imagine a solid object, homogeneous except for the presence within it of small particles of foreign material of different sizes. Interest lies in the size of the largest of these particles, and how that size relates to the volume of the solid. Direct observation inside the solid is impossible, but particles intersecting the surface can be seen in section. This is a problem with particular relevance to new high quality steels. All steels contain inclusions - small particles of impurity - which influence fatigue strength. In the new so-called clean steels the number and size of inclusions are much reduced and it becomes particularly important for safety reasons to estimate the likely size of the largest. Measurement of the cross-sections of inclusions exposed in sampled polished surfaces of the steel can be made reasonably routinely. Without the emphasis on the largest particles, inference about particle sizes on the basis of two-dimensional sections is a standard problem in stereology (Wicksell's corpuscle problem of 1925). The talk will describe a development which concentrates specifically on inferences about large particles, combining modern extreme value modelling with stereological ideas. Both likelihood-based and Bayesian approaches will be presented. The problem raises some general questions about the choice of models in the analysis of extremes. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%