Loss functions for estimation of extrema with an application to disease mapping

Canadian Journal of Statistics

Volumn 31, Issue 3, 2003, Pages 251-266

  Wright, Deanne L ^a   Stern, Hal S ^b   Cressie, Noel ^c  

^a PIONEER HI BRED INTERNATIONAL INC   (United States)

^b Ringgold Standard Institution Informatics   (United States)

^c OHIO STATE UNIVERSITY   (United States)

Author keywords

Bayes estimate; Posterior distribution; Relative risk; Squared error loss; Weighted ranks squared error loss

Indexed keywords

EID: 0742323766     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3316085     Document Type: Article

References (27)

1. L. Bernardinelli, D. G. Clayton & C. Montomoli (1995). Bayesian estimates of disease maps: How important are priors? Statistics in Medicine, 14, 2411-2431.
2. J. Besag (1974). Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society Series B, 36, 192-236.
3. J. Besag, J. York & A. Mollié (1991). Bayesian image restoration with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics, 43, 1-59.
4. N. E. Breslow & D. G. Clayton (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88, 9-25.
5. D. G. Clayton & L. Bernardinelli (1992). Bayesian methods for mapping disease risk. In Geographical and Environmental Epidemiology: Methods for Small-Area Studies (P. Elliot, J. Cuzick, D. English & R. Stern, eds.), Oxford University Press (for the World Health Organization Regional Office for Europe), pp. 205-220.
6. D. G. Clayton & J. M. Kaldor (1987). Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics, 43, 671-681.
7. N. Cressie (1992). Smoothing regional maps using empirical Bayes predictors. Geographical Analysis, 24, 75-95.
8. N. Cressie (1993). Statistics for Spatial Data, Revised edition. Wiley, New York.
9. N. Cressie & N. H. Chan (1989). Spatial modeling of regional variables. Journal of the American Statistical Association, 84, 393-401.
10. A. Gelman, J. B. Carlin, H. S. Stern & D. B. Rubin (1995). Bayesian Data Analysis. Chapman & Hall, New York.
11. A. Gelman & P. N. Price (1999). All maps of parameter estimates are misleading. Statistics in Medicine, 18, 3221-3224.
12. A. Gelman & D. B. Rubin (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457-511.
13. S. Geman & D. Geman (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
14. M. Ghosh (1992). Constrained Bayes estimation with applications. Journal of the American Statistical Association, 87, 533-540.
15. A. Lawson, A. Biggeri, C. Dean & L. Waller, eds. (2000). Disease Mapping with a Focus on Evaluation. Special issue of Statistics in Medicine, vol. 19, no. 17/18, pp. 2201-2593.
16. T. A. Louis (1984). Estimating a population of parameter values using Bayes and empirical Bayes methods. Journal of the American Statistical Association, 79, 393-398.
17. N. Mantel & C. R. Stark (1968). Computation of indirect-adjusted rates in the presence of confounding. Biometrics, 24, 997-1005.
18. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller & E. Teller (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-1092.
19. N. Metropolis & S. Ulam (1949). The Monte Carlo method. Journal of the American Statistical Association, 44, 335-341.
20. S. Richardson, C. Monfort, M. Green, G. Draper & C. Muirhead (1995). Spatial variation of natural radiation and childhood leukemia incidence in Great Britain. Statistics in Medicine, 14, 2487-2501.
21. W. Shen & T. A. Louis (1998). Triple-goal estimates in two-stage hierarchical models. Journal of the Royal Statistical Society Series B, 60, 455-471.
22. W. Shen & T. A. Louis (2000). Triple-goal estimates for disease mapping. Statistics in Medicine, 19, 2295-2308.
23. D. J. Spiegelhalter, A. Thomas & N. G. Best (1996). Computation on Bayesian graphical models. In Bayesian Statistics 5: Proceedings of the Fifth Valencia International Meeting, June 5-9, 1994 (J. M. Bernardo, J. O. Berger, A. P. Dawid & A. F. M. Smith, eds.), Oxford University Press, pp. 407-425.
24. H. S. Stern & N. Cressie (1995). Bayesian and constrained Bayesian inference for extremes in epidemiology. In Proceedings of the Epidemiology Section, American Statistical Association, pp. 11-20.
25. H. S. Stern & N. Cressie (1999). Inference for extremes in disease mapping. In Disease Mapping and Risk Assessment for Public Health (A. Lawson, A. Biggeri, D. Böhning, E. Lesaffre, J.-F. Viel & R. Bertollini, eds.), Wiley, Chichester, pp. 63-84.
26. H. S. Stern & N. Cressie (2000). Posterior predictive model checks for disease mapping models. Statistics in Medicine, 19, 2377-2397.
27. L. A. Waller, B. P. Carlin, H. Xia & A. E. Gelfand (1997). Hierarchical spatio-temporal mapping of disease incidence rates. Journal of the American Statistical Association, 92, 607-617.