Estimating a Nonstationary Spatial Structure Using Simulated Annealing

Journal of Computational and Graphical Statistics

Volumn 13, Issue 1, 2004, Pages 90-105

  Iovleff, Serge ^a   Perrin, Olivier ^b  

^a UNIV LILLE   (France)

^b UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Bijective space deformation; Constrained minimization; Delaunay triangulation

Indexed keywords

EID: 1842486865     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/1061860043100     Document Type: Article

References (25)

1. Aarts, E., and Korst, T. J. (1989), Simulated Annealing and Boltzman Machines Stochastic Approaches to Combinatorial Optimization and Neural Computing, New York: Wiley.
2. Azencott, R. (ed) (1992), Simulated Annealing: Parallelization Techniques, New York: Wiley.
3. Cressie, N. A. C. (1993), Statistics for Spatial Data (rev. ed.), New York: Wiley-Interscience.
4. Damian, D., Sampson, P. D., and Guttorp, P. (2000). "Bayesian Estimation of Semi-parametric Non-stationary Spatial Covariance Structures," Environmetrics, 12, 161-178.
5. Geman, D. (1990), Random Fields and Inverse Problem in Imaging, L.N.M. no. 1427, New York: Springer.
6. Geman, S., and Geman, D. (1984), "Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
7. Guttorp, P., and Sampson, P. D. (1994), "Methods for Estimating Heterogeneous Spatial Covariance Functions with Environmental Applications," in Handbook of Statistics XII: Environmental Statistics, eds. G. P. Patil and C. R. Rao, New York: Elsevier/North Holland, pp. 663-690.
8. Guttorp, P., Sampson, P. D., and Newman, K. (1992), "Nonparametric Estimation of Non-stationary Spatial Covariance Structure with Application to Monitoring Network Design," in Statistics in Environmental and Earth Sciences, eds. A. Walden and P. Guttorp, London: Edward Arnold, pp. 39-51.
9. Haario, H., and Saksman, E. (1991), "Simulated Annealing Process in General State Space," Advances in Applied Probability, 23, 866-893.
10. Hajek, B. (1988), "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, 13, 311-329.
11. Hwang, C.-R. (1980), "Laplace's Methods Revisited: Weak Convergence of Probability Measures," The Annals of Probability, 8, 1177-1182.
12. Høst, G., Omre, H., and Switzer, P. (1995), "Spatial Interpolation Errors for Monitoring Data," Journal of the American Statistical Association, 90, 853-861.
13. Kirkpatrick, S., Gelatt, Jr., C. D., and Vecchi, M. P. (1983), "Optimization by Simulated Annealing," Science, 220, 671-679.
14. Meiring, W. (1995), "Estimation of Heterogeneous Space-Time Covariance," PhD thesis, University of Washington, Seattle.
15. Meiring, W., Guttorp, P., and Sampson, P. D. (1998), "Computational Issues in Fitting Spatial Deformation Models for Heterogeneous Spatial Correlation," in Computing Science and Statistics, ed. D. W. Scott, 29, pp. 409-417.
16. Meiring, W., Monestiez, P., Sampson, P. D., and Guttorp, P. (1997), "Developments in the Modelling of Nonstationary Spatial Covariance Structure from Space-Time Monitoring Data," in Geostatistics Wollongong '96, eds. E. Y. Baafi and N. Schofield, 1, Amsterdam: Kluwer Academic Publishers, pp. 162-173.
17. Monestiez, P., Sampson, P. D., and Guttorp, P. (1993), "Modelling of Heterogeneous Spatial Correlation Structure by Spatial Deformation," Cahiers de Geostatistique, Fascicule 3, Compte Rendu des Journées de Géostatistique, 25-26 May 1993, Fontainebleau. Published by the École Nationale Supérieure des Mines de Paris.
18. Perrin, O., and Meiring, W. (1999), "Identifiability for Non-stationary Spatial Structure," Journal of Applied Probability, 36, 1244-1250.
19. Perrin, O., and Monestiez, P. (1998), "Modelling of Non-stationary Spatial Structure Using Parametric Radial Basis Deformations," in geoENV98, eds. A. Soares, J. Gómez-Hernandez, and R. Froidevaux, Amsterdam: Kluwer Academic Publishers, pp. 175-186.
20. Perrin, O., and Senoussi, R. (2000), "Reducing Non-stationary Random Fields to Stationary or Isotropy Using a Space Deformation," Statistics and Probability Letters, 48, 23-32.
21. Sampson, P., and Guttorp, P. D. (1992), "Nonparametric Estimation of Nonstationary Spatial Covariance Structure," Journal of the American Statistical Association, 87, 108-119.
22. Sampson, P. D., Guttorp, P., and Meiring, W. (1994), "Spatio-Temporal Analysis of Regional Ozone Data for Operational Evaluation of an Air Quality Model," in Proceedings of the Section on Statistics and the Environment, Alexandria, VA: American Statistical Association.
23. Schmidt, A. M., and O'Hagan, A. (2000), "Bayesian Inference for Nonstationary Spatial Covariance Structure via Spatial Deformations," to appear in Journal of the Royal Statistical Society Series B.
24. Shewchuk, J. R. (1996), "Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator," First Workshop on Applied Computational Geometry, Philadelphia, PA, ACM, pp. 124-133; available online from http://www.cs.cmu.edu/~quake/triangle.research.html.
25. Tierney, L. (1994), "Markov Chains for Exploring Posterior Distributions" (with discussion) The Annals of Statistics, 22, 1701-1762.