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Related Experiment Videos

Precision of circular systematic sampling.

L M Cruz-Orive1, X Gual-Arnau

  • 1Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Avda. Los Castros s/n, E-39005 Santander, Spain. lcruz@matesco.unican.es

Journal of Microscopy
|September 17, 2002
PubMed
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This summary is machine-generated.

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This study addresses predicting the precision of systematic sampling in stereology. A new method using a global symmetric covariogram model is presented, showing promise for periodic functions, especially with small sample sizes.

Area of Science:

  • Stereology
  • Geometric Probability
  • Sampling Theory

Background:

  • Unbiased stereological estimators often require isotropic orientation of test probes.
  • Systematic sampling of orientations is crucial for efficiency and practical application in stereology.
  • Common stereological tools like the planar nucleator and Buffon-Steinhaus method involve systematic sampling on circles or semicircles.

Purpose of the Study:

  • To develop and evaluate methods for predicting the precision of systematic sampling on circles and semicircles from a single sample.
  • To compare a classical prediction approach with a recent method based on a global symmetric covariogram model.
  • To incorporate local errors into the prediction model for periodic measurement functions.

Main Methods:

  • Systematic sampling on the circle and semicircle.

Related Experiment Videos

  • Classical prediction approach (G. Matheron).
  • New approach using a global symmetric model of the covariogram.
  • Incorporation of local errors into the covariogram model.

    • Main Results:

    • Two main approaches for predicting sampling precision exist: classical and covariogram-based.
    • The covariogram-based approach is effective for periodic measurement functions, particularly with small sample sizes.
    • The developed method incorporates local errors, enhancing its applicability.

    Conclusions:

    • The global symmetric covariogram model offers a satisfactory method for predicting stereological sampling precision.
    • The new approach is particularly advantageous for periodic functions and small sample sizes.
    • The study provides detailed examples of common stereological tools.