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Perfect simulation and inference for point processes given noisy observations

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Summary

The paper is concerned with the exact simulation of an unobserved true point process conditional on a noisy observation. We use dominated coupling from the past (CFTP) on an augmented state space to produce perfect samples of the target marked point process. An optimized coupling of the target chains makes the algorithm considerable faster than with the standard coupling used in dominated CFTP for point processes. The perfect simulations are used for inference and the results are compared to an ordinary Metropolis-Hastings sampler.

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Acknowledgements

Elke Thönnes thanks for the support by the EU TMR network ERB-FMRXCT96- 0096 and the Stochastic Centre at Chalmers University. Both authors acknowledge the support by the ESF program “Highly structured stochastic systems”. We are grateful to Ib Skovgaard, Wilfrid Kendall and Jesper Møller for inspiring discussions. We also thank Mats Rudemo for helpful comments, and the Danish Forest and Landscape Research Institute for access to the data.

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Authors and Affiliations

  1. Department of Mathematics and Physics, The Royal Veterinary and Agricultural University, Thorvaldsensvej 40, DK-1871, Frederiksberg C, Denmark

    Jens Lund

  2. Department of Statistics, University of Warwick, CV4 7AL, Coventry, UK

    Elke Thönnes

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  1. Jens Lund
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  2. Elke Thönnes
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Lund, J., Thönnes, E. Perfect simulation and inference for point processes given noisy observations. Computational Statistics 19, 317–336 (2004). https://doi.org/10.1007/BF02892063

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