Adaptive Gaussian Markov random fields with applications in human brain mapping

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 56, Issue 3, 2007, Pages 327-345

  Brezger, A ^a   Fahrmeir, L ^a   Hennerfeind, A ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

Adaptive weights; Human brain mapping; Inhomogeneous Markov random fields; Markov chain Monte Carlo methods; Space varying coefficient models; Spatiotemporal modelling

Indexed keywords

EID: 34249054454     PISSN: 00359254     EISSN: 14679876     Source Type: Journal    
DOI: 10.1111/j.1467-9876.2007.00580.x     Document Type: Article

References (25)

1. Assunção, R. (2003) Space varying coefficient models for small areal data. Environmetrics, 14, 453 473.
2. Baladandayuthapani, V., Mallick, B. K. Carroll, R. J. (2005) Spatially adaptive Bayesian penalized regression splines. J. Computnl Graph. Statist., 14, 378 394.
3. Brezger, A. (2005) Bayesian P-splines in structured additive regression models. Dissertation. University of Munich, Munich.
4. Carlin, B. P Banerjee, S 2003) Hierarchical multivariate CAR models for spatio-temporally correlated survival data. In Bayesian Statistics 7 (eds J. M. Bernardo, A. P. Dawid, J. O. Berger, M. West, D. Heckerman, M. J. Bayarri and A. F. M. Smith pp. 45 64. Oxford : Oxford University Press.
5. Carter, C. Kohn, R. (1996) Markov chain Monte Carlo for conditionally Gaussian state space models. Biometrika, 83, 589 601.
6. Fahrmeir, L. Gössl, C. (2002) Semiparametric Bayesian models for human brain mapping. Statist. Modllng, 2, 235 250.
7. Friston, K. J., Holmes, A. P., Poline, J.-B., Grasby, P., Williams, S. C. R., Frackowiak, R. S. J. Turner, R. (1995) Analysis of fMRI time-series revisited. NeuroImage, 2, 45 53.
8. Geman, D. Reynolds, G. (1992) Constrained restoration and the recovery of discontinuities. IEEE Trans. Pattn Anal. Mach. Intell., 14, 367 383.
9. Genovese, C. R. (2000) A Bayesian time-course model for functional magnetic resonance imaging data (with discussion). J. Am. Statist. Ass., 95, 691 719.
10. Gössl, C. (2001) Bayesian models in functional magnetic resonance imaging: approaches for human brain mapping. Dissertation. University of Munich, Munich.
11. Gössl, C., Auer, D. P. Fahrmeir, L. (2000) Dynamic models in fMRI. Magn. Resnce Med., 43, 72 81.
12. Gössl, C., Auer, D. P. Fahrmeir, L. (2001) Bayesian spatio-temporal inference in functional magnetic resonance imaging. Biometrics, 57, 554 562.
13. Jin, X., Carlin, B. P. Banerjee, S. (2005) Generalized hierarchical multivariate CAR models for areal data. Biometrics, 61, 950 961.
14. Knorr-Held, L. (1999) Conditional prior proposals in dynamic models. Scand. J. Statist., 26, 129 144.
15. Knorr-Held, L 2003) Some remarks on Gaussian Markov random field models for disease mapping. In Highly Structured Stochastic Systems (eds P. Green, N. Hjort S. Richardson). Oxford : Oxford University Press.
16. Knorr-Held, L. Rue, H. (2002) On block updating in Markov random field models for disease mapping. Scand. J. Statist., 29, 597 614.
17. Lang, S. Brezger, A. (2004) Bayesian P-splines. J. Computnl Graph. Statist., 13, 183 212.
18. Lang, S., Fronk, E.-M. Fahrmeir, L. (2002) Function estimation with locally adaptive dynamic models. Computnl Statist., 17, 479 500.
19. Lu, H., Reilly, C. S., Banerjee, S Carlin, B. P 2005) Bayesian areal wombling via adjacency modeling. Research Report 2005-015. Division of Biostatistics, University of Minnesota, Minneapolis.
20. Ma, H., Virnig, B Carlin, B. P 2005) Spatial methods in geographic administrative data analysis. Research Report 2005-016. Division of Biostatistics, University of Minnesota, Minneapolis.
21. Rue, H. (2001) Fast sampling of Gaussian Markov random fields. J. R. Statist. Soc. B, 63, 325 338.
22. Rue, H. Held, L. (2005) Gaussian Markov Random Fields; Theory and Applications. Boca Raton : Chapman and Hall-CRC.
23. Smith, M. Fahrmeir, L. (2007) Spatial Bayesian variable selection with application to functional magnetic resonance imaging. J. Am. Statist. Ass., to be published.
24. Smith, M., Pütz, B., Auer, D Fahrmeir, L 2003) Assessing brain activity through spatial Bayesian variable selection. NeuroImage, 20, 812 815.
25. Tabelow, K., Polzehl, J Spokoiny, V 2005) Analysing fMRI experiments with structural adaptive smoothing procedures. Preprint 1079. Weierstrass Institute for Applied Analysis and Stochastics, Berlin.