Hidden Markov models and disease mapping

Journal of the American Statistical Association

Volumn 97, Issue 460, 2002, Pages 1055-1070

  Green, Peter J ^a   Richardson, Sylvia ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b IMPERIAL COLLEGE SCHOOL OF MEDICINE   (United Kingdom)

Author keywords

Allocation; Bayesian hierarchical model; Disease mapping; Finite mixture distributions; Heterogeneity; Hidden Markov models; Markov chain Monte Carlo; Poisson mixtures; Potts model; Reversible jump algorithms; Semiparametric model; Spatial mixtures

Indexed keywords

EID: 0036970574     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214502388618870     Document Type: Article

References (33)

1. Austin, D. F., and Reynolds, P. (1996), "Laryngeal Cancer," in Cancer Epidemiology and Prevention (2nd ed.), eds. D. Schottenfeld and J. F. Fraumeni, Oxford, UK: Oxford University Press, pp. 619-636.
2. Aykroyd, R. G., and Zimeras, S. (1999), "Inhomogeneous Prior Models for Image Reconstruction," Journal of the American Statistical Association, 94, 934-946.
3. Besag, J. (1986), "On the Statistical Analysis of Dirty Pictures" (with discussion), Journal of the Royal Statistical Society, Ser. B, 48, 259-302.
4. Besag, J., York, J., and Mollié, A. (1991), "Bayesian Image Restoration With Applications in Spatial Statistics" (with discussion), Annals of the Institute of Mathematical Statistics, 43, 1-59.
5. Best, N. G., Arnold, R. A., Thomas, A., Waller, L. A., and Conlon, E. M. (1999), "Bayesian Models for Spatially Correlated Disease and Exposure Data," in Bayesian Statistics 6, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, UK: Oxford University Press, pp. 131-156.
6. Carroll, R. J., Roeder, K., and Wasserman, L. (1999), "Flexible Parametric Measurement Error Models," Biometrics, 55, 44-54.
7. Clayton, D., and Bernardinelli, L. (1992), "Bayesian Methods for Mapping Disease Risk," in Geographical and Environment Epidemiology: Methods for Small Area Studies, eds. P. Elliott, J. Cuzick, D. English, and R. Stern, Oxford, UK: Oxford University Press, pp. 205-220.
8. Clifford, P. (1986), Discussion of "On the Statistical Analysis of Dirty Pictures" by J. Besag, Journal of the Royal Statistical Society, Ser. B, 48, 284.
9. Denison, D. G. T., and Holmes, C. C. (2001), "Bayesian Partitioning for Estimating Disease Risk," Biometrics, 51, 143-149.
10. Elliott, P., Wakefield, J. C., Best, N. G., and Briggs, D. J. (2000), Spatial Epidemiology: Methods and Applications, Oxford, UK: Oxford University Press.
11. Fernández, C., and Green, P. J. (2002), "Modelling Spatially Correlated Data via Mixtures: A Bayesian Approach," Journal of the Royal Statistical Society, Ser. B, 64, to appear (part 4).
12. Gelman, A., and Meng, X.-L. (1998), "Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling," Statistical Science, 13, 163-185.
13. Green, P. J. (1995), "Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination," Biometrika, 82, 711-732.
14. Greenland, S., and Robins, J. (1994), "Ecological Studies: Biases, Misconceptions, and Counterexamples," American Journal of Epidemiology, 139, 747-760.
15. Johnson, V. E. (1994), "A Model for Segmentation and Analysis of Noisy Images," Journal of the American Statistical Association, 89, 230-241.
16. Knorr-Held, L., and Raßer, G. (2000), "Bayesian Detection of Clusters and Discontinuities in Disease Maps," Biometrics, 56, 13-21.
17. Knorr-Held, L., and Rue, H. (2002), "On Block Updating in Markov Random Field Models for Disease Mapping," Scandinavian Journal of Statistics, 29, in press.
18. Künsch, H. R. (2001), "Stale Space and Hidden Markov Models," in Complex Stochastic Systems, eds. O. E. Barndorff-Nielsen, D. R. Cox, and C. Klüppelberg, London: Chapman and Hall/CRC, pp. 109-173.
19. Lawson, A. B., and Clark, A. (2002), "Spatial Mixture Relative Risk Models Applied to Disease Mapping," Statistics in Medicine, 21, 359-370.
20. McLachlan, G., and Peel, D. (2000), Finite Mixture Models, Chichester, UK: Wiley.
21. Mollié, A. (1996), "Bayesian Mapping of Disease," in Markov Chain Monte Carlo in Practice, eds. W. Gilks, S. Richardson, and D. J. Spiegelhalter, London: Chapman and Hall, pp. 359-379.
22. Ogata, Y., and Tanemura, M. (1984), "Likelihood Analysis of Spatial Point Patterns," Journal of the Royal Statistical Society, Ser. B, 46, 496-518.
23. Rezvani, A., Mollié, A., Doyon, F., and Sancho-Garnier, H. (1997), Atlas de la Mortalité par Cancer en France, Période 1986-1993, Paris: Editions INSERM.
24. Richardson, S., and Green, P. J. (1997), "On Bayesian Analysis of Mixtures With an Unknown Number of Components" (with discussion), Journal of the Royal Statistical Society, Ser. B, 59, 731-792.
25. Robert, C. P., Rydén, T., and Titterington, D. M. (2000), "Bayesian Inference in Hidden Markov Models Through the Reversible Jump Markov Chain Monte Carlo Method," Journal of the Royal Statistical Society, Ser. B, 62, 57-75.
26. Roeder, K., Carroll, R. J., and Lindsay, B. G. (1996), "A Semiparametric Mixture Approach to Case-Control Studies With Errors in Covariables." Journal of the American Statistical Association, 91, 722-732.
27. Rydén, T., and Titterington, D. M. (1998), "Computational Bayesian Analysis of Hidden Markov Models," Journal of Computational and Graphical Statistics, 7, 194-211.
28. Stephens, M. (2000), "Bayesian Analysis of Mixture Models With an Unknown Number of Components - An Alternative to Reversible Jump Methods," Annals of Statistics, 28, 40-74.
29. Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and van der Linde, A. (2002), "Bayesian Measures of Model Complexity and Fit," Journal of the Royal Statistical Society, Ser. B, 64, to appear.
30. Titterington, D. M., Smith, A. F. M., and Makov, U. E. (1985), Statistical Analysis of Finite Mixture Distributions, Chichester, UK: Wiley.
31. Tjelmeland, H., and Besag, J. (1998). "Markov Random Fields With Higher-Order Interactions," Scandinavian Journal of Statistics, 25, 415-433.
32. Viallefont, V., Richardson, S., and Green, P. J. (2002), "Bayesian Analysis of Poisson Mixtures," Nonparametric Statistics, 14, 181-202.
33. Wakefield, J., and Morris, S. (1999), "Spatial Dependence and Errors-in-Variables in Environmental Epidemiology," in Bayesian Statistics 6, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, UK: Oxford University Press, pp. 657-684.