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Rejection- and importance-sampling-based perfect simulation for Gibbs hard-sphere models

Part of: Limit theorems Probabilistic methods, simulation and stochastic differential equations Stochastic processes Algorithms - Computer Science

Published online by Cambridge University Press:  08 October 2021

Sarat Moka ,
Sandeep Juneja  and
Michel Mandjes
Sarat Moka*
Affiliation:
University of Queensland
Sandeep Juneja*
Affiliation:
Tata Institute of Fundamental Research
Michel Mandjes*
Affiliation:
University of Amsterdam
*
*Postal address: School of Mathematics and Physics, Coopers Road, St Lucia, QLD, Australia 4072. Email: s.babumoka@uq.edu.au
**Postal address: Homi Bhabha Road, Colaba, Mumbai, India 400005. Email: juneja@tifr.res.in
***Postal address: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands. Email: m.r.h.mandjes@uva.nl
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Abstract

Coupling-from-the-past (CFTP) methods have been used to generate perfect samples from finite Gibbs hard-sphere models, an important class of spatial point processes consisting of a set of spheres with the centers on a bounded region that are distributed as a homogeneous Poisson point process (PPP) conditioned so that spheres do not overlap with each other. We propose an alternative importance-sampling-based rejection methodology for the perfect sampling of these models. We analyze the asymptotic expected running time complexity of the proposed method when the intensity of the reference PPP increases to infinity while the (expected) sphere radius decreases to zero at varying rates. We further compare the performance of the proposed method analytically and numerically with that of a naive rejection algorithm and of popular dominated CFTP algorithms. Our analysis relies upon identifying large deviations decay rates of the non-overlapping probability of spheres whose centers are distributed as a homogeneous PPP.

Keywords

Exact simulationdominated coupling from the pastlarge deviationsnon-overlapping probability

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60G55: Point processes 60F10: Large deviations 68W40: Analysis of algorithms
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 3 , September 2021 , pp. 839 - 885
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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