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Authors: Jiancang Zhuang
Title: [download]
(1297)
Likelihood-based detection of cluster centers for Neyman–Scott point processes
Reference: Vol. 8, Issue 3, Sep 2018
Submitted 2017-12-18, Accepted 2018-09-08
Type: Article
Abstract:

This study deals with the problem of estimating the unobservable cluster centers for a special type of Neyman–Scott point processes, in which the cluster sizes (numbers of members in each cluster) are distributed according to the Poisson distribution. The key point of the solution is the conversion among different forms of conditional intensities, λ(t | ·)dt = P{N[t,t + dt) = 1 | ·} = E[N[t,t + dt) | ·], where · represents a σ-algebra generated by some information from the process N. Some recursive formulae associated with the filtering gain (information gain represented by the ratio of the likelihood of the point process when we know more information to the likelihood when we know less) are derived. These recursive equations can be solved numerically by using Monte Carlo integration. The proposed method is illustrated by two simulation experiments, a purely temporal and a multi-type spatiotemporal case.

Paper: [download]
(1297)
Likelihood-based detection of cluster centers for Neyman–Scott point processes
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Paper: Creative Commons Attribution 3.0 Unported License
Code: Commons GNU General Public License License
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