Does a Gibbs sampler approach to spatial Poisson regression models outperform a single site MH sampler?

Computational Statistics and Data Analysis

Volumn 52, Issue 9, 2008, Pages 4184-4202

  Gschlößl, Susanne ^a   Czado, Claudia ^b  

^a Munchener Ruckversicherungs Gesell   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; AUTOCORRELATION; COMPUTATIONAL METHODS; INSURANCE; MATHEMATICAL MODELS; REGRESSION ANALYSIS;

DATA AUGMENTATION; GIBBS SAMPLER; POISSON REGRESSION MODEL;

POISSON DISTRIBUTION;

EID: 42749094403     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2008.02.020     Document Type: Article

References (28)

1. Besag J., and Kooperberg C. On conditional and intrinsic autoregressions. Biometrika 82 (1995) 733-746
2. Christensen O.F., Roberts G.O., and Sköld M. Robust MCMC methods for spatial GLMM's. Journal of Computational and Graphical Statistics 15 (2006) 1-17
3. Christensen O.F., and Waagepetersen R. Bayesian prediction of spatial count data using generalized linear mixed models. Biometrics 58 (2002) 280-286
4. Czado, C., Prokopenko, S., 2007. Modeling transport mode decisions using hierarchical binary spatial regression models with cluster effects. Statistical Modelling (in press)
5. Diggle P.J., Tawn J.A., and Moyeed R.A. Model-based geostatistics. Journal of the Royal Statistical Society, Series C 47 3 (1998) 299-350 (With discussion and a reply by the authors)
6. Dimakos X.K., and Frigessi A. Bayesian premium rating with latent structure. Scandinavian Actuarial Journal 3 (2002) 162-184
7. Frühwirth-Schnatter, S., Frühwirth, R., Held, L., Rue, H., 2007. Improved auxiliary mixture sampling for hierarchical models of non-Gaussian data. Preprint. Department for Applied Statistics, Johannes Kepler University, Linz, IFAS Research Paper Series, 2007-25
8. Frühwirth-Schnatter S., and Rudolf Frühwirth. Auxiliary mixture sampling with applications to logistic models. Computational Statistics and Data Analysis 51 (2007) 3509-3528
9. Frühwirth-Schnatter S., and Wagner H. Auxiliary mixture sampling for parameter-driven models of time series of small counts with applications to state space modelling. Biometrika 93 (2006) 827-841
10. Frühwirth-Schnatter S., and Wagner H. Data augmentation and Gibbs sampling for regression models of time series of small counts. Student 5 (2006) 221-234
11. Frühwirth-Schnatter S. Efficient Bayesian parameter estimation. In: Harvey A.C., Koopman S.J., and Shephard N. (Eds). State Space and Unobserved Component Models (2004), Cambridge Univ. Press, Cambridge 123-151
12. Gelfand A.E., Sahu S.K., and Carlin B.P. Efficient parametrisations for normal linear mixed models. Biometrika 82 3 (1995) 479-488
13. Geyer C.J. Practical Markov Chain Monte Carlo. Statistical Science 7 4 (1992) 473-511
14. Gschlößl, S., Czado, C., 2007a. Modelling count data with overdispersion and spatial effects. Statistical Papers. To appear online available under 10.1007/s00362-006-0031-6
15. Gschlößl S., and Czado C. Spatial modelling of claim frequency and claim size in non-life insurance. Scandinavian Actuarial Journal 107 3 (2007) 202-225
16. Haran M., Hodges J.S., and Carlin B. Accelerating computation in Markov random field models for spatial data via structured MCMC. Journal of Computational and Graphical Statistics 12 2 (2003) 249-264
17. Kass R.E., Carlin B., Gelman A., and Neal R. Markov Chain Monte Carlo in practice: A roundtable discussion. The American Statistician 52 (1998) 93-100
18. Knorr-Held L., and Rue H. On block updating in Markov random field models for disease mapping. Scandinavian Journal of Statistics. Theory and Applications 29 (2002) 325-338
19. Liu J.S., Wong W.H., and Kong A. Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes. Biometrika 81 1 (1994) 27-40
20. Mikosch T. Non-Life Insurance Mathematics. An Introduction with Stochastic Processes (2004), Springer, New York
21. Paciorek C.J. Computational techniques for spatial logistic regression with large data sets. Computational Statistics and Data Analysis 51 (2007) 3631-3653
22. Papaspiliopoulos O., Roberts G.O., and Sköld M. Non-centered parameterizations for hierarchical models and data augmentation. Bayesian Statistics vol. 7 (Tenerife, 2002) (2003), Oxford Univ. Press, New York 307-326 With a discussion by Alan E. Gelfand, Ole F. Christensen and Darren J. Wilkinson, and a reply by the authors
23. Pettitt A.N., Weir I.S., and Hart A.G. A conditional autoregressive Gaussian process for irregularly spaced multivariate data with application to modelling large sets of binary data. Statistics and Computing 12 4 (2002) 353-367
24. Roberts G.O., and Sahu S.K. Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler. Journal of the Royal Statistical Society, B 59 2 (1997) 291-317
25. Rue H. Fast sampling of Gaussian Markov random fields. Journal of the Royal Statistical Society. Series B. Statistical Methodology 63 4 (2001) 597-614
26. Rue H., Steinsland I., and Erland S. Approximating hidden Gaussian Markov random fields. Journal of the Royal Statistical Society. Series B. Statistical Methodology 66 4 (2004) 877-892
27. Sargent D.J., Hodges J.S., and Carlin B.P. Structured Markov Chain Monte Carlo. Journal of Computational and Graphical Statistics 9 (2000) 217-234
28. Sun D., Tsutakawa R.K., Kim H., and He Z. Bayesian analysis of mortality rates with disease maps. Statistics in Medicine 19 (2000) 2015-2035