Books about geostatistics:

  • Chiles and Delfiner (1999). Geostatistics; modelling spatial uncertainty. Wiley, New York.

  • Cressie (1993). Statistics for spatial data. Revised edition. Wiley, New York.

    Books about MCMC:

  • Robert, C. P. and Casella, G. (1999). Monte Carlo statistical methods. Springer-Verlag, New York.

  • Gilks, W., Richardson, S. and Spiegelhalter, D. (eds.) (1996). Markov chain Monte Carlo in practice. Chapman and Hall, London.

    Articles about generalised linear spatial models:

  • Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998). Model-based geostatistics (with discussion). Appl. Statist. 47, 299-350.

  • Zhang, H. (2002). On estimation and prediction for spatial generalised linear mixed models. Biometrics 58, 129-136.

  • Christensen, O. F. and Waagepetersen, R. P. (2002). Bayesian prediction of spatial count data using generalized linear mixed models. Biometrics 58, 280-286.

  • Diggle, P. J., Moyeed, R. A., Rowlingson, B., Thomson, M. (2002). Childhood malaria in the Gambia : a case-study in model-based geostatistics. Applied statistics 51, 493-506.

  • Zhang, H. (2003). Optimal interpolation and the effectiveness of cross-validating variogram in spatial generalised linear mixed models. Journal of computational and graphical statistics 12, 698-713.

  • Ole F. Christensen, Gareth O. Roberts and Martin Sköld (2006). Robust Markov chain Monte Carlo methods for spatial generalised linear mixed models. Journal of Computational and Graphical Statistics 15 1-17. (Abstract).

  • Christensen, O. F. (2004). Monte Carlo maximum likelihood in model-based geostatistics. Journal of computational and graphical statistics 13, 702-718.

  • Diggle, P. J., Ribeiro Jr, P. J. and Christensen, O. F. (2003). An introduction to model-based geostatistics. In : Spatial statistics and computational methods (ed. J. Møller), Springer Verlag, 43-86.

  • Christensen, O. F. and Ribeiro Jr, P. J. (2002). geoRglm - a package for generalised linear spatial models. R News, 2(2), 26-28. ISSN 1609-3631. (Download )

    Only the last three articles are reflected reasonably well in the implementation in package geoRglm.

    Short FAQ:

  • The MCMC-algorithm seems not to be mixing well. What to do ? The general solution is to make longer run's. It is not unusual for me when doing Bayesian inference to make 2,000,000 iterations, storing every 2,000. The problem is most pronounced when phi is random and a normal prior with a large variance is used for beta. The solution here is to use the flat prior for beta instead of the normal.

  • Is inference for the nugget implemented ? The relative nugget tausq.rel is fixed when doing Bayesian inference. I have no plans allowing a prior on tausq.rel for two reasons : 1) I do not know how meaningful priors should look like; 2) For computational reasons, having a discrete prior on both phi and tausq.rel requires that a large number of matrices are precomputed and stored. Maximum likelihood estimation of the relative nugget is possible using either MCMC-MLE, which is implemented in the function likfit.glsm, or MCMC-EM, which has not yet been implemented.

  • Are improper priors dangerous to use ? Not always, but the resulting posterior distribution may not exist (be improper). For the priors implemented in the geoRglm the posterior is proper, apart from when using the reciprocal prior for sigmasq where the posterior becomes improper.

  • Problem with random seed : If you get an execution error like ``.Random.seed[0] is not a valid Normal type'', the problem is that the random seed is not defined. A solution is f.ex. to call rnorm(1) once before calling the function in geoRglm.

  • Multivariate analysis : is not implemented in the package. In particular the analysis of the Malaria data in Diggle et al. (2002) cannot be replicated using geoRglm.

  • Markov chain Monte Carlo EM : as in Zhang 2002 is not yet implemented.

    Return to the geoRglm home page.

    Last revision: 6 april 2006.