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Random Fraction of a Biased Sample: old models and a new one

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In materials science, stereological problems occur naturally when 2D pictures are observed, where 3D information is actually required. This talk introduces a model that was developed for precipitates in steel. The model can be called a `directed cut cylinder model’. In an opaque volume, directed circular cylinders are randomly distributed and a cross-section of the volume is observed, perpen- dicular to the base of the cylinders. Observations then consist of rectangular pro files of (some of the) cylinders. The height of the cut-cylinder is observed exactly; its diameter not, since the cylinder could be cut close to the center or close to the boundary of its base. Aim is to estimate relevant (from a materials science point of view) aspects of the joint distribution of radius and height of the cylinders based on the observed rectangular pro files.

The model is related to a class of (univariate) models that can be called `random fraction of a biased sample’ models. Examples include the linear probe problem, Wicksell’s corpuscle problem and Hampel’s migrating birds problem. In this presentation, the model will be introduced and estimation problems posed. Moreover, estimators will be de fined and asymptotic properties given.

Joint work with Kimberly McGarrity (TU Delft and M2i) and Jilt Sietsma (TU Delft, Department of Materials Science).

This talk is part of the Statistics series.

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