Objective Bayesian analysis for geostatistical Student-t processes

References

• Azzalini, A. and Capitanio, A., 2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. Journal of the Royal Statistical Society, Series B, 65 (2), 367–389.
   Google Scholar
• Banerjee, S., Carlin, B.P., and Gelfand, A.E., 2014. Hierarchical modeling and analysis for spatial data. Boca Raton, Florida, USA: Chapman and Hall/CRC.
   Google Scholar
• Berger, J.O. and Bernardo, J.M., 1991. On the development of reference priors. Bayesian Statistics, 4, 35–60.
   Google Scholar
• Berger, J.O., De Oliveira, V., and Sansó, B., 2001. Objective Bayesian analysis of spatially correlated data. Journal of the American Statistical Association, 96 (456), 1361–1374. doi:10.1198/016214501753382282
   Web of Science ®Google Scholar
• Bevilacqua, M., et al., 2020. Non-Gaussian geostatistical modeling using (skew) t processes. Scandinavian Journal of Statistics. doi:10.1111/sjos.12447
   Web of Science ®Google Scholar
• Branco, M.D., Genton, M.G., and Liseo, B., 2013. Objective Bayesian analysis of skew-t distributions. Scandinavian Journal of Statistics, 40 (1), 63–85. doi:10.1111/j.1467-9469.2011.00779.x
   Web of Science ®Google Scholar
• Cressie, N.A.C., 1993. Statistics for spatial data. revised edition. New York, USA: John Wiley & Sons, Inc.
   Google Scholar
• De Oliveira, V., 2007. Objective Bayesian analysis of spatial data with measurement error. Canadian Journal of Statistics, 35 (2), 283–301. doi:10.1002/cjs.5550350206
   Web of Science ®Google Scholar
• Diggle, P. and Ribeiro, P., 2007. Model-based geostatistics. New York, USA: Springer Series in Statistics.
   Google Scholar
• Fonseca, T.C., Ferreira, M.A.R., and Migon, H.S., 2008. Objective Bayesian analysis for the Student-t regression model. Biometrika, 101 (1), 252. doi:10.1093/biomet/asu001
   Google Scholar
• Gelman, A. and Rubin, D.B., 1992. Inference from iterative simulation using multiple sequences. Statistical Science, 7 (4), 457–472. doi:10.1214/ss/1177011136
   Google Scholar
• Geweke, J., 1993. Bayesian treatment of the independent Student-t linear model. Journal of Applied Econometrics, 8 (S1), S19–S40. doi:10.1002/jae.3950080504
   Web of Science ®Google Scholar
• Gradshtejn, I.S. and Ryzhik, I.M., 1965. Table of integrals, series and products. The American Society of Mechanical Engineers (ASME), USA: Academic Press.
   Google Scholar
• He, D., Sun, D., and He, L., 2020. Objective Bayesian analysis for the Student-t linear regression. Bayesian Analysis.
   Google Scholar
• Ho, H.J., et al., 2012. Some results on the truncated multivariate t distribution. Journal of Statistical Planning and Inference, 142 (1), 25–40. doi:10.1016/j.jspi.2011.06.006
   Web of Science ®Google Scholar
• Kaufman, C.G. and Shaby, B.A., 2013. The role of the range parameter for estimation and prediction in geostatistics. Biometrika, 100 (2), 473–484. doi:10.1093/biomet/ass079
   Web of Science ®Google Scholar
• Kazianka, H. and Pilz, J., 2012. Objective Bayesian analysis of spatial data with uncertain nugget and range parameters. Canadian Journal of Statistics, 40 (2), 304–327. doi:10.1002/cjs.11132
   Web of Science ®Google Scholar
• Keefe, M.J., Ferreira, M.A.R., and Franck, C.T., 2019. Objective Bayesian analysis for Gaussian hierarchical models with intrinsic conditional autoregressive priors. Bayesian Analysis, 14(1), 181–209. doi:10.1214/18-BA1107
   Web of Science ®Google Scholar
• Kennedy, M.C. and O’Hagan, A., 2001. Bayesian calibration of computer models. Journal of the Royal Statistical Society, Series B, 63 (3), 425–464. doi:10.1111/1467-9868.00294
   Web of Science ®Google Scholar
• Kotz, S. and Nadarajah, S., 2004. Multivariate t-distributions and their applications. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Lange, K.L., Little, R.J., and Taylor, J., 1989. Robust statistical modeling using the t distribution. Journal of the American Statistical Association, 84 (408), 881–896.
   Web of Science ®Google Scholar
• Muré, J., 2020. Propriety of the reference posterior distribution in Gaussian process modeling.
   Google Scholar
• Oliveira, M.C.N., 2003. Métodos de estimação de parâmetros em modelos geoestatísticos com diferentes estruturas de covariâncias: uma aplicação ao teor de cálcio no solo. Thesis (PhD). ESALQ/USP/Brasil.
   Google Scholar
• Ordoñez, A., et al., 2021. OBASpatial: objective Bayesian analysis for spatial regression models. R package version 1.8.
   Google Scholar
• Palacios, M.B. and Steel, M.F.J., 2006. Non-Gaussian Bayesian geostatistical modeling. Journal of the American Statistical Association, 101 (474), 604–618. doi:10.1198/016214505000001195
   Web of Science ®Google Scholar
• Parisi, A. and Liseo, B., 2018. Objective Bayesian analysis for the multivariate skew-t model. Statistical Methods and Applications, 27, 277–295.
   Web of Science ®Google Scholar
• Paulo, R., 2005. Default priors for Gaussian processes. The Annals of Statistics, 33 (2), 556–582. doi:10.1214/009053604000001264
   Web of Science ®Google Scholar
• Ren, C., Sun, D., and He, C., 2012. Objective Bayesian analysis for a spatial model with nugget effects. Journal of Statistical Planning and Inference, 142 (7), 1933–1946. doi:10.1016/j.jspi.2012.02.034
   Web of Science ®Google Scholar
• Ren, C., Sun, D., and Sahu, S.K., 2013. Objective Bayesian analysis of spatial models with separable correlation functions. Canadian Journal of Statistics, 41 (3), 488–507. doi:10.1002/cjs.11186
   Web of Science ®Google Scholar
• Ribeiro, P.J., Jr, et al., 2020. geor: analysis of geostatistical data. R package version 1.8-1, Available from: https://CRAN.R-project.org/package=geoR
   Google Scholar
• Spiegelhalter, D.J., et al., 2002. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society. Series B, Statistical Methodology, 64 (4), 583–639. doi:10.1111/1467-9868.00353
   Web of Science ®Google Scholar
• Stein, C., 1985. On the coverage probability of confidence sets based on a prior distribution. Banach Center Publications, 16, 485–514.
   Google Scholar
• Tomazella, V., et al., 2020. Reference Bayesian analysis for the generalized lognormal distribution with application to survival data. Statistics and Its Interface, 13 (1), 139–149. doi:10.4310/SII.2020.v13.n1.a12
   Web of Science ®Google Scholar
• Tomazella, V.L.D., et al., 2021. Bayesian reference analysis for the generalized normal linear regression model. Symmetry, 13 (5), 856. doi:10.3390/sym13050856
   Google Scholar
• Villa, C. and Walker, S.G., 2014. Objective prior for the number of degrees of freedom of a t distribution. Bayesian Analysis, 9 (1), 197–220. doi:10.1214/13-BA854
   Web of Science ®Google Scholar
• Zellner, A., 1976. Bayesian and non-Bayesian analysis of the regression model with multivariate Student-t error terms. Journal of the American Statistical Association, 71 (354), 400–405.
   Web of Science ®Google Scholar