Perfect simulation of some point processes for the impatient user

Advances in Applied Probability

Volumn 31, Issue 1, 1999, Pages 69-87

  Thönnes, Elke ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Area interaction process; Continuum random cluster model; Gibbs sampler; Markov chain Monte Carlo; Penetrable spheres mixture process; Perfect simulation; Point processes; User impatience bias

Indexed keywords

EID: 0032593236     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1029954267     Document Type: Article

References (19)

1. BADDELEY, A. J. and Van Lieshout, M. N. M. (1995). Area-interactionpointprocesses. Ann. Inst. Statist. Math. 47, 601-619.
2. CHAYES, J. T., CHAYES, L. and Kotecky, R. (1995). The analysis of the Widom-Rowlinson model by stochastic geometric methods. Commun. Math. Phys. 172, 551-569.
3. FILL, J. A. (1998). An interruptible algorithm for perfect sampling via Markov chains. Ann. Appl. Prob. 8, 131-162.
4. Gilks, W. R., Richardson, S. and Spiegelhalter, D. J. (1996). Markov Chain Monte Carlo In Practice. Chapman & Hall, London.
5. HAggstrom, O., Van Lieshout, M. N. M. and MØLLER, J. (1996). Characterisation results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes. Aalborg Mathematics Department Research Report R-96-2040. To appear in Bernoulli.
6. HAMMERSLEY, J. M., Lewis, J. W. E. and Rowlinson, J. S. (1975). Relationships between the multinomial and poisson models of stochastic processes, and between the canonical and grand canonical ensembles in statistical mechanics, with illustrations and Monte Carlo methods for the penetrable spheres model of liquid-vapourequilibrium. Sankhya A, 37, 457-491.
7. KENDALL, W. S. (1999). Perfect simulation for the area-interaction point process. In Probability Towards 2000, ed. L. Accardi and C. C Heyde. Springer, New York, pp. 218-234.
8. KENDALL, W. S. and MØLLER, J. (1999). Perfect Metropolis-Hastings simulation of locally stable point processes. Preprint 347, Department of Statistics, University of Warwick.
9. KLEIN, W. (1982). Potts-model formulation of continuumpercolation. Physical ReviewB 26, 2677-2678.
10. LINDVALL, T. (1992). Lectures on the Coupling Method. Wiley, New York.
11. Meyn, S. P. and TWEEDIE, R. L. (1994). Computablebounds for geometric convergenceof Markovchains. Ann. Appl. Prob. 4, 981-1011.
12. MØLLER, J. (1997). Markov chain Monte Carlo and spatial point processes. In Stochastic Geometry: Likelihood and Computation, ed. O. Barndorff-Nielsen, W. S. Kendall, and M. N. M. Van Lieshout. Chapman & Hall, BocaRaton, FL, pp. 141-172.
13. PROPP, J. G., WILSON, D. B. (1998). Coupling from the past: a user’s guide. In Miscrosurveys in Discrete Probability, ed. D. Aldous and J. Propp. (DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 41). Amer. Math. Soc., Providence, RI, pp. 181-192.
14. PROPP, J. G. and WILSON, D. B. (1996). Exact sampling with coupled Markov chains and applications to statistical mechanics. Random StructuresAlgorithms 9, 223-252.
15. ROBERTS, G. O. and POLSON, N. G. (1994). On the geometric convergenceof the Gibbs sampler. J. Royal Statist. Soc. B, 56, 377-384.
16. ROWLINSON, J. S (1980). Penetrable spheres model of liquid vapour equilibrium. Adv. Chemical Phys. 41, 1-57.
17. ROWLINSON, J. S. (1990). Probability densities for some one-dimensionalproblems in statistical mechanics. In Disorderin Physical Systems. Ed. G. R. Grimmet and D. J. A. Welsh. Clarendon Press, Oxford, pp. 261-276.
18. Saloff-Coste, L. (1997). Simple examples of the use of Nash inequalities for finite Markov chains. In Stochastic Geometry: Likelihood and Computation, ed. O. Barndorff-Nielsen, W. S. Kendall and M. N. M. Van Lieshout. Chapman & Hall, Boco Raton, FL, pp. 365-400.
19. WIDOM, B. and ROWLINSON, J. S. (1970). New model for the study of liquid-vapor phase transitions. J. Chemical Phys. 52, 1670-1684.