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Maximum likelihood estimation for cooperative sequential adsorption

Part of: Inference from stochastic processes Special processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Mathew D. Penrose  and
Vadim Shcherbakov
Mathew D. Penrose*
Affiliation:
University of Bath
Vadim Shcherbakov*
Affiliation:
University of Bath and Moscow State University
*
∗ Postal address: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. Email address: [email protected]
∗∗ Postal address: Laboratory of Large Random Systems, Faculty of Mechanics and Mathematics, Moscow State University, Glavnoe Zdanie Leninskie Gory, 119991, Moscow, Russia. Email address: [email protected]
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Abstract

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We consider a model for a time series of spatial locations, in which points are placed sequentially at random into an initially empty region of ℝd, and given the current configuration of points, the likelihood at location x for the next particle is proportional to a specified function βk of the current number (k) of points within a specified distance of x. We show that the maximum likelihood estimator of the parameters βk (assumed to be zero for k exceeding some fixed threshold) is consistent in the thermodynamic limit where the number of points grows in proportion to the size of the region.

Keywords

Cooperative sequential adsorptionspace–time point processmaximum likelihood estimationthermodynamic limitincreasing domain asymptoticlaw of large numbers

MSC classification

Primary: 62M30: Spatial processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 41 , Issue 4 , December 2009 , pp. 978 - 1001
Copyright
Copyright © Applied Probability Trust 2009 

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