[Statlist] Special Talk with Johanna Ziegler, Wednesday September, 1, 2010, 14.15h, HG G19.1

[Susanne Kaiser-Heinzmann]

Seminar für Statistik, ETH Zürich, Prof. Hansruedi Künsch:

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We are glad to 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 Ziegler, 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 
brain
structures 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 depen-
dence 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 ˆv, rather than estimation of the 
distribution of ˆv;
see e.g. Cruz-Orive (1999); Gundersen et al. (1999); Garc´ıa-Fi ˜nana 
and Cruz-Orive
(2004); Ziegel et al. (2010). We use a bootstrap method to obtain a 
consistent
estimator of the distribution of ˆv 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 perfor-
mance 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.
Garc´ıa-Fi ˜nana, 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., Kiˆeu, 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). Sys-
tematic sampling with errors in sample locations. Biometrika , 97, 1–13.


*Please find also the abstract in the attachment.*


-- 
ETH Zürich
Sekretriat 		  sekretariat at stat.math.ethz.ch
Seminar für Statistik
Rämistrasse 101, HG G10.3	  phone: +41 44 6326518
CH-8092 Zurich, Switzerland	  fax  : +41 44 6321228
  

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