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Keywords:

  • Brain;
  • Cavalieri design;
  • fractional smoothness constant;
  • measurement function;
  • particle number;
  • slab;
  • slice;
  • stereology;
  • systematic sampling;
  • variance prediction;
  • volume

Summary

A general variance predictor is presented for a Cavalieri design with slices of an arbitrary thickness t ≥ 0. So far, prediction formulae have been available either for measurement functions with smoothness constant q = 0, 1, … , and t ≥ 0, or for fractional q ∈ [0, 1] with t = 0. Because the possibility of using a fractional q adds flexibility to the variance prediction, we have extended the latter for any q ∈ [0, 1] and t ≥ 0. Empirical checks with previously published human brain data suggest an improved performance of the new prediction formula with respect to the hitherto available ones.