1. Cardinality estimation for random stopping sets based on Poisson point processes.
- Author
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Privault, Nicolas
- Subjects
- *
POISSON processes , *POINT processes , *RANDOM sets , *POINT set theory , *POISSON distribution , *STOCHASTIC geometry , *MARTINGALES (Mathematics) - Abstract
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 SĖ 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. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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