| Issue |
ESAIM: PS
Volume 25, 2021
|
|
|---|---|---|
| Page(s) | 87 - 108 | |
| DOI | https://doi.org/10.1051/ps/2021004 | |
| Published online | 23 March 2021 | |
Cardinality estimation for random stopping sets based on Poisson point processes*
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University,
21 Nanyang Link,
Singapore
637371, Singapore.
** Corresponding author: nprivault@ntu.edu.sg
Received:
1
March
2020
Accepted:
14
January
2021
We construct unbiased estimators for the distribution of the number of points inside random stopping sets based on a Poisson point process. Our approach is based on moment identities for stopping sets, showing that the random count of points inside the complement S̅ of a stopping set S has a Poisson distribution conditionally to S. The proofs do not require the use of set-indexed martingales, and our estimators have a lower variance when compared to standard sampling. Numerical simulations are presented for examples such as the convex hull and the Voronoi flower of a Poisson point process, and their complements.
Mathematics Subject Classification: 60G55 / 60D05 / 60G40 / 60G57 / 60G48
Key words: Stochastic geometry / Poisson point process / factorial moments / stopping sets / random convex hull / Voronoi tessellation
© EDP Sciences, SMAI 2021
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