[Statlist] REMINDER Special Talk with Johanna Ziegel, Wednesday, September 1, 2010, 14.15h, ETH Zürich, HG G19.1

[Susanne Kaiser-Heinzmann]

REMINDER

Seminar für Statistik, ETH Zürich, Prof. Hansruedi Künsch:
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We announce the following special talk

*Wednesday, September 1, 2010, 14.15 - 16.00, ETH Zürich, HG G 19.1*

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with Johanna Ziegel, The University of Melbourne
joint work with Peter Hall, The University of Melbourne

Title:
*Distribution estimators and confidence intervals for Cavalieri estimators*

Abstract:
Volume estimators based on Cavalieri’s principle are widely used in the 
bio-sciences. For example in neuroscience, where volumetric measurements 
of brainstructures are of interest, systematic samples of serial 
sections are obtained by magnetic resonance imaging or by a physical 
cutting procedure. The volume is then estimated by the sum over the 
areas of the structure of interest in the section planes multiplied by 
the width of the sections. Assessing the precision of such volume 
estimates is a question of great practical importance, but statistically 
a challenging task due to the strong spatial dependence of the data and 
typically small sample sizes. The approach we take is more ambitious 
than earlier methodologies, the goal of which has been estimation of the 
variance of a volume estimator \hat{v}, rather than estimation of the 
distribution of \hat{v} ; see e.g. Cruz-Orive (1999); Gundersen et al. 
(1999); García-Fiñana and Cruz-Orive (2004); Ziegel et al. (2010). We 
use a bootstrap method to obtain a consistent estimator of the 
distribution of \hat{v} conditional on the observed data. Confidence 
intervals are then derived from the distribution estimate. We treat the 
case where serial sections are exactly periodic as well as when the 
physical cutting procedure introduces errors in the placement of the 
sampling points. To illustrate the performance of our method we conduct 
a simulation study with synthetic data and also apply our results to 
real data sets.

References
Cruz-Orive, L. M. (1999). Precision of Cavalieri sections and slices 
with local errors.
J. Microsc., 193, 182–198.
García-Fiñana, M. and Cruz-Orive, L. M. (2004). Improved variance 
prediction for systematic sampling on R. Statistics , 38(3), 243–272.
Gundersen, H. J. G., Jensen, E. B. V., Kiêu, K., and Nielsen, J. (1999). 
The efficiency of systematic sampling – reconsidered. J. Microsc., 193, 
199–211.
Ziegel, J., Baddeley, A., Dorph-Petersen, K.-A., and Jensen, E. B. V. 
(2010). Systematic sampling with errors in sample locations. Biometrika 
, 97, 1–13.

This abstract is also to be found under the following link:
http://stat.ethz.ch/talks/research_seminar

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