A conditional autoregressive Gaussian process for irregularly spaced multivariate data with application to modelling large sets of binary data

Statistics and Computing

Volumn 12, Issue 4, 2002, Pages 353-367

  Pettitt, A N ^a   Weir, I S ^b   Hart, A G ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

^b UNIVERSITY OF THE WEST OF ENGLAND   (United Kingdom)

Author keywords

Bayesian analysis; Binary data; Conditional autoregression; Markov chain Monte Carlo; Multivariate data; Spatial statistics; Spatio temporal

Indexed keywords

EID: 0141457201     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020792130229     Document Type: Article

References (22)

1. Adler R.J. 1981. The Geometry of Random Fields. Wiley, Chichester.
2. Belyaev Yu.K. 1961. Continuity and Hölder continous conditions for sample functions of stationary Gaussian processes. In: Proc. Fourth Berkeley Symp. Math. Statist. Prob. University of California Press, Berkely, Vol. 2, pp. 23-33.
3. Besag J.E. 1974. Spatial interaction and the statistical analysis of lattice systems (with discussion). J. Roy. Statist. Soc. B 36: 192-236.
4. Besag J. and Higdon D. 1999. Bayesian analysis of agricultural field experiments (with discussion). J. Roy. Statist. Soc. B 61: 691-746.
5. Besag J.E. and Kooperberg C. 1995. On conditional and intrinsic autoregressions. Biometrika 82: 733-746.
6. Best N.G., Cowles M.K., and Vines S.K. 1995. CODA Manual version 0.30. MRC Biostatistics Unit, Cambridge, UK.
7. Chib S. and Greenberg E. 1998. Analysis of multivariate probit models. Biometrika 85: 347-361.
8. Cressie N.A.C. 1993. Statistics for Spatial Data, Rev. Edition. Wiley, New York.
9. Cressie N.A.C. and Huang H.-C. 1999. Classes of nonseparable, spatio-temporal stationary covarince function. J. Am. Statist. Assoc. 94: 1330-1340.
10. Dempster A.P. 1972. Covariance selection. Biometrics 28: 157-175.
11. Diggle P.J., Tawn J.A., and Moyeed R.A. 1998. Model-based geostatistics (with discussion). Appl. Statist. 47: 299-350.
12. Ecker M.D. and Gelfand A.E. 1997. Bayesian variogram modelling for an isotropic spatial process. J. Agric. Biol. Environ. Statist. 2: 347-369.
13. Gilks W.R., Richardson S., and Spiegelhalter D.J. 1996. Markov Chain Monte Carlo in Practice. Chapman & Hall, London.
14. Graybill F.A. 1983. Matrices with Applications in Statistics, 2nd Edition. Wadsworth, California.
15. He Z. axld Sun D. 2000. Hierarchical bayes estimation of hunting success rates with spatial correlations. Biometrics 56: 360-367.
16. Heidelberger P. and Welch P. 1983. Simulation run length control in the presence of an initial transient. Operations Research 7: 493-497.
17. Mardia K.V. 1988. Multi-dimensional multivariate Gaussian Markov random fields with application to image processing. J. Multivariate Analysis 24(2): 265-284.
18. McCormack B. 1995. Timber inventory manual for the native forests of Queensland. Technical Report, Queensland Dept. Primary Industries-Forest Service, Brisbane, Queensland.
19. Thompson J., Bean A., Dillewaard H., Sparshott K., Grimshaw P., Dowling R., Stephens K., Price R., and Stanley T. 1996. Methodolgy for vegetation survey and mapping for eastern Queensland. Technical Report, Queensland Dept. Environment and Heritage, Brisbane, Queensland.
20. Weir I.S. and Pettitt A.N. 1999. Spatial modelling for binary data using a hidden conditional autoregressive Gaussian process: A multivariate extension of the probit model. Statistics and Computing 9: 77-86.
21. Weir I.S. and Pettitt A.N. 2000. Binary probability maps using a hidden conditional autoregressive Gaussian process with an application to Finnish common toad data. Appl. Statist. 49: 473-484.
22. Wikle C.R. and Cressie N. 1999. A dimension-reduced approach to space-time Kalman filtering. Biometrika 86: 815-829.