Markov chain Monte Carlo methods for fitting spatiotemporal stochastic models in plant epidemiology

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 46, Issue 2, 1997, Pages 215-233

  Gibson, Gavin J ^a,b  

^a BIOMATHEMATICS AND STATISTICS SCOTLAND   (United Kingdom)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

Markov chain Monte Carlo method; Plant epidemiology; Spatiotemporal stochastic models

Indexed keywords

EID: 0039377949     PISSN: 00359254     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9876.00061     Document Type: Article

References (33)

1. Bennett, R. J. (1979) Spatial Time Series. London: Pion.
2. Besag, J. (1977) Discussion on Spatial contact models for ecological and epidemic spread (by D. Mollison). J. R. Statist. Soc. B, 39, 315-316.
3. Besag, J. and Green, P. J. (1993) Spatial statistics and Bayesian computation. J. R. Statist. Soc. B, 55, 25-37.
4. Brower, R. C., Furman, M. A. and Moshe, M. (1978) Critical exponents for the Reggeon quantum spin model. Phys. Lett. B, 76, 213-219.
5. Buckland, S. T. and Elston, D. A. (1993) Empirical models for the spatial distribution of wildlife. J. Appl. Ecol., 30, 478-495.
6. Buttell, L., Cox, J. T. and Durrett, R. (1993) Estimating the critical values of stochastic growth models. J. Appl. Probab., 30, 455-461.
7. Chatfield, C. (1995) Model uncertainty, data mining and statistical inference (with discussion). J. R. Statist. Soc. A, 158, 419-466.
8. Cliff, A. D. and Ord, J. K. (1981) Spatial Processes: Models and Applications. London: Pion.
9. Cox, J. T. and Durrett, R. (1981) Some limit theorems for percolation processes with necessary and sufficient conditions. Ann. Probab., 9, 583-603.
10. _ (1988) Limit theorems for the spread of epidemics and forest fires. Stoch. Processes Appl., 30, 171-191.
11. Diggle, P. J. (1983) Statistical Analysis of Spatial Point Patterns. London: Academic Press.
12. Draper, D. (1995) Assessment and propagation of model uncertainty (with discussion). J. R. Statist. Soc. B, 57, 45-97.
13. Fleiss, J. L. (1971) Measuring nominal scale agreement among many raters. Psychol. Bull., 76, 378-382.
14. Gelfand, A. E. and Smith, A. F. M. (1990) Sampling-based approaches to calculating marginal densities. J. Am. Statist. Ass., 85, 398-409.
15. Gibson, G. J. and Austin, E. J. (1996) Fitting and testing spatio-temporal stochastic models with applications in plant epidemiology. Plant Path., 45, 172-184.
16. Gottwald, T. R., Reynolds, K. M., Campbell, C. L. and Timmer, L. W. (1992) Spatial and spatio-temporal autocorrelation analysis of citrus canker epidemics in citrus nurseries and groves in Argentina. Phytopathology, 82, 843-851.
17. Green, P. J. (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711-732.
18. Hastings, W. K. (1970) Monte Carlo sampling methods using Markov Chains, and their applications. Biometrika, 57, 97-109.
19. Hughes, G. and Madden, L. V. (1993) Using the beta-binomial distribution to describe aggregated patterns of disease incidence. Phytopathology, 83, 759-763.
20. Marcus, R., Svetlana, F., Talpaz, H., Salomon, R. and Bar-Joseph, M (1984) On the spatial distribution of citrus tristeza virus disease. Phytoparasitica, 12, 45-52.
21. Metropolis, M., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953) Equations of state calculation by fast computing machines. J. Chem. Phys., 21, 1087-1093.
22. Mollison, D. (1977) Spatial contact models for ecological and epidemic spread (with discussion). J. R. Statist. Soc. B, 39, 283-326.
23. _ (1986) Modelling biological invasions: chance, explanation, prediction. Phil. Trans. R. Soc. Lond. B, 314, 675-693.
24. Ohtsuki, T. and Keyes, T. (1986) Kinetic growth percolation: epidemic processes with immunization Phys. Rev. A, 33, 1223-1232.
25. Reynolds, K. M. and Madden, L. V. (1988a) Analysis of epidemics using spatio-temporal autocorrelation. Phytopathology, 78, 240-246.
26. _ (1988b) Spatio-temporal analysis of epidemic development of leather rot of strawberry. Phytopathology, 78, 246-252.
27. Ripley, B. D. (1987) Stochastic Simulation. Chichester: Wiley.
28. Shaw, M. W. (1994) Modelling stochastic processes in plant pathology. A. Rev. Phytpath., 32, 523-544.
29. _ (1995) Simulation of population expansion and spatial pattern when individual dispersal distributions do not decline exponentially with distance. Proc. R. Soc. Lond. B, 259, 243-248.
30. Smith, A. F. M and Roberts, G. O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. R. Statist. Soc. B, 55, 3-23.
31. Smyth, G. K., Chakraborty, S., Clark, R. G. and Pettitt, A. N. (1992) A stochastic model for anthracnose development in Stylosanthes scabra. Phytopathology, 82, 1267-1272.
32. Tierney, L. (1994) Markov chains for exploring posterior distributions. Ann. Statist., 22, 1701-1762.
33. Zadoks, J. C. and van den Bosch, F. (1994) On the spread of plant disease: a theory on foci. A. Rev. Phytpath., 32, 503-521.