On the precision of the conditionally autoregressive prior in spatial models

Biometrics

Volumn 59, Issue 2, 2003, Pages 317-322

  Hodges, James S ^a   Carlin, Bradley P ^a   Fan, Qiao ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b MINNEAPOLIS MEDICAL RESEARCH FOUNDATION   (United States)

Author keywords

Bayesian analysis; Gaussian Markov random field model; Improper prior; Markov chain Monte Carlo (MCMC) methods; Periodontal data

Indexed keywords

BAYESIAN NETWORKS; GAUSSIAN DISTRIBUTION; IMAGE SEGMENTATION; MARKOV PROCESSES; MONTE CARLO METHODS; SPATIAL VARIABLES MEASUREMENT;

AUTO-REGRESSIVE; BAYESIAN ANALYSIS; GAUSSIAN MARKOV RANDOM FIELD MODELS; IMPROPER PRIOR; L 1 NORM; MARKOV CHAIN MONTE CARLO METHOD; PERIODONTAL DATA; PRECISION PARAMETER; SPATIAL DATA; SPATIAL MODELLING;

STOCHASTIC SYSTEMS;

BAYESIAN ANALYSIS; PRECISION; SPATIAL DATA;

ARTICLE; BIOSTATISTICS; DATA ANALYSIS; DISEASE MAPPING; HUMAN; MAJOR CLINICAL STUDY; MONTE CARLO METHOD; NORMAL DISTRIBUTION; PERIODONTICS; PROBABILITY; REGRESSION ANALYSIS; STATISTICAL ANALYSIS; STATISTICAL MODEL; STATISTICAL PARAMETERS;

EID: 0037869543     PISSN: 0006341X     EISSN: None     Source Type: Journal    
DOI: 10.1111/1541-0420.00038     Document Type: Article

References (15)

1. Bernardinelli, L., Pascutto, C., Best, N. G., and Gilks, W. R. (1997). Disease mapping with errors in covariates. Statistics in Medicine 16, 741-752.
2. Besag, J. and Higdon, D. (1999). Bayesian analysis of agricultural field experiments (with discussion). Journal of the Royal Statistical Society, Series B 61, 691-746.
3. Besag, J. and Kooperberg, C. (1995). On conditional and intrinsic autocorrelation. Biometrika 82, 733-746.
4. Besag, J., York, J. C., and Mollié A. (1991). Bayesian image restoration, with two applications in spatial statistics (with discussion). Annals of the Institute of Statistical Mathematics 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 (with discussion). In Bayesian Statistics 6, J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith (eds), 131-156. Oxford: Oxford University Press.
6. Carlin, B. P. and Louis, T. A. (2000). Bayes and Empirical Bayes Methods for Data Analysis, 2nd edition. Boca Raton, Florida: Chapman and Hall/CRC Press.
7. Clayton, D. G. and Kaldor, J. M. (1987). Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics 43, 671-681.
8. Darby, M. L. and Walsh, M. M. (1995). Periodontal and Oral Hygiene Assessment. Dental Hygiene Theory and Practice. Philadelphia: W. B. Saunders.
9. Fan, Q. (2002). A conditionally autoregressive (CAR) model applied to a periodontal data set. M. S. thesis, Division of Biostatistics, University of Minnesota.
10. Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences (with discussion). Statistical Science 7, 457-511.
11. Golub, G. H. and Van Loan, C. F. (1996). Matrix Computations, 3rd edition. Baltimore, Maryland: The Johns Hopkins University Press.
12. Knorr-Held, L. (2002). Some remarks on Gaussian Markov random field models for disease mapping. In Highly Structured Stochastic Systems, P. Green, N. Hjort, and S. Richardson (eds), 260-264. Oxford: Oxford University Press.
13. Spiegelhalter, D. J., Thomas, A., Best, N., and Gilks, W. R. (1995a). BUGS: Bayesian inference using Gibbs sampling, version 0.50. Technical report, Medical Research Council Biostatistics Unit, Institute of Public Health, Cambridge University.
14. Spiegelhalter, D. J., Thomas, A., Best, N., and Gilks, W. R. (1995b). BUGS examples, version 0.50. Technical Report, Medical Research Council Biostatistics Unit, Institute of Public Health, Cambridge University.
15. Stuart, A. and Ord, J. K. (1994). Kendall's Advanced Theory of Statistics. Volume 1: Distribution Theory, 6th edition. London: Arnold.