ESTIMATION OF SAMPLE SPACING IN STOCHASTIC PROCESSES

Authors

  • Anders Rønn-Nielsen Department of Mathematical Sciences, University of Copenhagen http://orcid.org/0000-0003-3941-9354
  • Jon Sporring Department of Computer Science, University of Copenhagen
  • Eva B. Vedel Jensen Department of Mathematics, Aarhus University

DOI:

https://doi.org/10.5566/ias.1681

Keywords:

Lévy-based modelling, Monte Carlo methods, random fields, stereology, section distance, systematic sampling, variance, variogram

Abstract

Motivated by applications in electron microscopy, we study the situation where a stationary and isotropic random field is observed on two parallel planes with unknown distance. We propose an estimator for this distance. Under the tractable, yet flexible class of Lévy-based random field models, we derive an approximate variance of the estimator. The estimator and the approximate variance perform well in two simulation studies.

References

Baddeley A, Jensen E B V (2005). Stereology for statisticians. Monographs on statistics and applied probability. Chapman & Hall/CRC Press.

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Hellmund G, Prokesová M, Jensen E B V (2008). Lévy-based Cox point processes. Adv Appl Prob. 40:603-29.

Jónsdóttir K Ý, Jensen E B V (2013). Lévy-based error prediction in circular systematic sampling. Image Anal Stereol 32:117-25.

Jónsdóttir K Ý, Rønn-Nielsen A, Mouridsen K, Jensen E B V (2013). Lévy-based modelling in brain imaging. Scand J Stat. 40(3):511-29.

Jónsdóttir K Ý, Schmiegel J, Jensen E B V (2008). Lévy-based growth models. Bernoulli 14(1):62-90.

Kendall M G, Stuart A (1977). The advanced theory of statistics, Vol. 1. Distribution theory, 4th edn. Griffin, London.

Sporring J, Khanmohammadi M, Darkner S, Nava N, Nyengaard J R, Jensen E B V (2014). Estimating the thickness of ultra thin sections for electron microscopy by image statistics. Proceedings of the 2014 IEEE International symposium on biomedical imaging, Beijing, 29 April - 2 May 2014, 157-60.

Ziegel J, Baddeley A, Dorph-Petersen K-A, Jensen E B V (2010). Systematic sampling with errors in sample locations. Biometrika 97:1-13.

Ziegel J, Jensen E B V, Dorph-Petersen K-A (2011). Variance estimation for generalized Cavalieri estimators. Biometrika 98:187-98.

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Published

2017-03-31

Issue

Vol. 36 No. 1 (2017)

Section

Original Research Paper

License

Copyright (c) 2017 Image Analysis & Stereology

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Rønn-Nielsen, A., Sporring, J., & B. Vedel Jensen, E. (2017). ESTIMATION OF SAMPLE SPACING IN STOCHASTIC PROCESSES. Image Analysis and Stereology, 36(1), 43-49. https://doi.org/10.5566/ias.1681