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Coupling from the past (CFTP) methods have been used to generate perfectsamples from finite Gibbs hard-sphere models, an important class of spatialpoint processes, which is a set of spheres with the centers on a bounded regionthat are distributed as a homogeneous Poisson point process (PPP) conditionedthat spheres do not overlap with each other. We propose an alternativeimportance sampling based rejection methodology for the perfect sampling ofthese models. We analyze the asymptotic expected running time complexity of theproposed method when the intensity of the reference PPP increases to infinitywhile the (expected) sphere radius decreases to zero at varying rates. Wefurther compare the performance of the proposed method analytically andnumerically with a naive rejection algorithm and popular dominated CFTPalgorithms. Our analysis relies upon identifying large deviations decay ratesof the non-overlapping probability of spheres whose centers are distributed asa homogeneous PPP.

Rejection and Importance Sampling based Perfect Simulation for Gibbs hard-sphere models