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SUMMARY:Random Fraction of a Biased Sample: old models and a new one - Geu
 rt Jongbloed\, TU Delft\, EURANDOM
DTSTART:20121123T160000Z
DTEND:20121123T170000Z
UID:TALK40803@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:In materials science\, stereological problems occur naturally 
 when 2D pictures\nare observed\, where 3D information is actually required
 . This talk introduces a\nmodel that was developed for precipitates in ste
 el. The model can be called a\n`directed cut cylinder model'. In an opaque
  volume\, directed circular cylinders\nare randomly distributed and a cros
 s-section of the volume is observed\, perpen-\ndicular to the base of the 
 cylinders. Observations then consist of rectangular\nprofiles of (some of
  the) cylinders. The height of the cut-cylinder is observed\nexactly\; its
  diameter not\, since the cylinder could be cut close to the center or\ncl
 ose to the boundary of its base. Aim is to estimate relevant (from a mater
 ials\nscience point of view) aspects of the joint distribution of radius a
 nd height of\nthe cylinders based on the observed rectangular profiles.\n
 \nThe model is related to a class of (univariate) models that can be calle
 d `random\nfraction of a biased sample' models. Examples include the linea
 r probe problem\, Wicksell's corpuscle problem and Hampel's migrating bird
 s problem. In\nthis presentation\, the model will be introduced and estima
 tion problems posed.\nMoreover\, estimators will be defined and asymptoti
 c properties given.\n\nJoint work with Kimberly McGarrity (TU Delft and M2
 i) and Jilt Sietsma (TU\nDelft\, Department of Materials Science).
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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