Kendall, Wilfrid S., Shen, Yuan and Thönnes, Elke (2006) N-fold way simulated tempering for pairwise interaction point processes. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

Preview

PDF WRAP_kendall_06-11w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (405Kb)

Abstract

Pairwise interaction point processes with strong interaction are usually difficult to sample. We discuss how Besag lattice processes can be used in a simulated tempering MCMC scheme to help with the simulation of such processes. We show how the N-fold way algorithm can be used to sample the lattice processes efficiently and introduce the N-fold way algorithm into our simulated tempering scheme. To calibrate the simulated tempering scheme we use the Wang-Landau algorithm.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Point processes
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2006
Volume:	Vol.2006
Number:	No.11
Number of Pages:	21
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	GR/S52780/01 (EPSRC)
References:	[1] Y.P. Atchade and J. Liu. The Wang-Landau algorithm for Monte Carlo computation in general state spaces. Technical Report, 2004. [2] J. Besag, R. Milne and S. Zachary. Point process Limits of lattice processes. Journal of Applied Probability, 19:210-216,1982. [3] A.B. Bortz, M.H. Kalos and J.L. Lebowitz. A new algorithm for Monte Carlo simulation of Ising spin systems. Journal of Computational Physics, 17:10–18, 1975. [4] O. Capp´e, C.P. Robert and T. Ryd´en. Reversible jump MCMC converging to birth-and-death MCMC and more general continuous time samplers. Journal of the Royal Statistical Society, Series B,65:679-700, 2002. [5] P. Clifford and G. Nicholls. Comparison of birth-and-death and Metropolis- Hastings Markov chain Monte Carlo for the Strauss process. Department of Statistics, Oxford University. Manuscript, 1994. [6] P.J. Diggle. Statistical Analysis of Spatial Point Patterns. Academic Press. New York, 1983. [7] A.E. Gelfand and A.F.M. Smith. Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398– 409. 1990. [8] C. Geyer. Markov chain Monte Carlo maximum likelihood. In P. Keramidas, editor, Computer Science and Statistics, Proceedings of the 23rd Interface, 156-163. Interface Foundation, Fairfax Station, 1991. [9] C. Geyer and J. Møller. Simulation procedures and likelihood inference for spatial birth and death processes. Scandinavian Journal of Statistics, 21:359- 373. 1994. [10] C.J. Geyer and E.A. Thompson. Annealing Markov Chain Monte Carlo with applications to ancestral inference. Journal of the American Statistical Association, 90:909-920.1995. [11] M. Goulard, P. Grabarnik and A. S¨arkk¨a. Parameter estimation for marked Gibbs point processes through the pseudo-likelihood method. Scandinavian Journal of Statistics, 23:365–379,1996. [12] D. Higdon, H. Lee and Z. Bi. A Bayesian approach to characterizing uncertainty in inverse problems using coarse and fine scale information. IEEE Transactions on Signal Processing, 50:389-399, 2002. [13] M.A. Hurn and C. Jennison. A study of simulated annealing and a revised cascade algorithm for image reconstruction. Statistics and Computing. 5:175- 190, 1995. [14] D. Kandel, E. Domany and A. Brandt, Simulations without critical slowing down: Ising and three-state Potts models. Physical Review, Series B. 40: 330-344, 1989. [15] W. S. Kendall and J. Møller. Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes. Advances in Applied Probability, 32: 844-865, 2000. [16] W.S. Kendall and R.G. Wilson. Ising models and multi-resolution quad trees. Advances in Applied Probability. 35: 96-122, 2003. [17] M.N.M. van Lieshout and R.S. Stoica. Perfect simulation for marked point processes. To appear in Computational Statistics and Data Analysis, 2006. [18] J. Liu and C. Sabatti. Generalized Gibbs Sampler and Multigrid Monte Carlo for Bayesian Computation. Biometrika, 87:353-369, 2000. [19] E. Marinari and G. Parisi. Simulated tempering: a new Monte Carlo scheme. Europhysics Letters, 19: 451-458, 1992. [20] A. Sokal. Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms. Cours de Troisieme Cycle de la Physique en Suisse Romande. 1989 [21] D.J. Strauss. A model for clustering. Biometrika, 63:467-475, 1975. [22] F.Wang and D.P. Landau. Efficient, multiple-range random walk to calculate the density of states. Physical Reviews Letters, 86: 2050-2053. 2001.
URI:	http://wrap.warwick.ac.uk/id/eprint/35568

Request changes to a record

Actions (login required)

View Item