Volume 25, 2021
|Page(s)||87 - 108|
|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,
** Corresponding author: email@example.com
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.