A Skewed and Heavy-Tailed Latent Random Field Model for Spatial Extremes

References

• Abramowitz, M., and Stegun, I. A. (1970), Handbook of Mathematical Functions, Washington, DC: Bureau of Standards.
   Google Scholar
• Adler, R. J. (1981), The Geometry of Random Fields, New York: Wiley.
   Google Scholar
• Allard, D., and Naveau, P. (2007), “A New Spatial Skew-Normal Random Field Model,” Communications in Statistics—Theory and Methods, 36, 1821–1834.
   Web of Science ®Google Scholar
• Arellano-Valle, R. B., and Azzalini, A. (2006), “On the Unification of Families of Skew-Normal Distributions,” Scandinavian Journal of Statistics, 33, 159–188.
   Web of Science ®Google Scholar
• Azzalini, A., and Dalla Valle, A. (1996), “The Multivariate Skew-Normal Distribution,” Biometrika, 83, 715–726.
   Web of Science ®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, 93, 1361–1374.
   Web of Science ®Google Scholar
• Billingsley, P. (1986), Probability and Measure (2nd ed.), New York: Wiley.
   Google Scholar
• Carroll, S. S., and Cressie, N. (1996), “A Comparison of Geostatistical Methodologies Used to Estimate Snow Water Equivalent,” Water Resources Bulletin, 32, 267–278.
   Google Scholar
• Casson, E., and Coles, S. G. (1999), “Spatial Regression Models for Sample Extremes,” Extremes, 1, 449–468.
   Google Scholar
• Coles, S. G. (2001), An Introduction to Statistical Modeling of Extreme Values, London: Springer-Verlag.
   Google Scholar
• Cooley, D., Nychka, D., and Naveau, P. (2007), “Bayesian Spatial Modeling of Extreme Precipitation Return Levels,” Journal of the American Statistical Association, 102, 824–840.
   Web of Science ®Google Scholar
• Cooley, D. S., Cisewski, J., Erhardt, R. J., Jeon, S., Mannshardt-Shamseldin, E. C., Omolo, B. O., and Sun, Y. (2012), “A Survey of Spatial Extremes: Measuring Spatial Dependence and Modeling Spatial Effects,” Revstat, 10, 135–165.
   Web of Science ®Google Scholar
• Cressie, N. A. (1991), Statistics for Spatial Data, New York: Wiley-Interscience.
   Google Scholar
• Davison, A. C., Padoan, S., and Ribatet, M. (2012), “Statistical Modelling of Spatial Extremes,” Statistical Science, 27, 161–186.
   Web of Science ®Google Scholar
• De Oliveira, V., Kedem, B., and Short, D. A. (1997), “Bayesian Prediction of Transformed Gaussian Random Fields,” Journal of the American Statistical Association, 92, 1422–1433.
   Web of Science ®Google Scholar
• Fawcett, L., and Walshaw, D. (2014), “Estimating the Probability of Simultaneous Rainfall Extremes Within a Region: A Spatial Approach,” Journal of Applied Statistics, 41, 959–976.
   Web of Science ®Google Scholar
• Fuentes, M., Henry, J., and Reich, B. (2013), “Nonparametric Spatial Models for Extremes: Application to Extreme Temperature Data,” Extremes, 16, 75–101.
   PubMed Web of Science ®Google Scholar
• Gaetan, C., and Grigoletto, M. (2007), “A Hierarchical Model for the Analysis of Spatial Rainfall Extremes,” Journal of Agricultural, Biological and Environmental Statistics, 12, 434–449.
   Web of Science ®Google Scholar
• Gelman, A., Carlin, J., Stern, H., and Rubin, D. (2004), Bayesian Data Analysis, New York: Chapman & Hall.
   Google Scholar
• Genton, M., and Zhang, H. (2012), “Identifiability Problems in Some Non-Gaussian Spatial Random Fields,” Chilean Journal of Statistics, 3, 171–179.
   Google Scholar
• González-Farías, G., Dominguez-Molina, J. A., and Gupta, A. K. (2004), “Additive Properties of Skew-Normal Random Vectors,” Journal of Statistical Planning and Inference, 126, 521–534.
   Web of Science ®Google Scholar
• Handcock, M. S., and Stein, M. L. (1993), “A Bayesian Analysis of Kriging,” Technometrics, 35, 403–410.
   Web of Science ®Google Scholar
• Hosseini, F., Eidsvik, J., and Mohammadzadeh, M. (2011), “Approximate Bayesian Inference in Spatial GLMM With Skew Normal Latent Variables,” Computational Statistics and Data Analysis, 55, 1791–1806.
   Web of Science ®Google Scholar
• Kano, Y. (1994), “Consistency Property of Elliptical Probability Density Functions,” Journal of Multivariate Analysis, 51, 139–147.
   Web of Science ®Google Scholar
• Kim, H., and Mallick, B. K. (2003), “A Note on Bayesian Spatial Prediction Using the Elliptical Distribution,” Statistics and Probability Letters, 64, 271–276.
   Web of Science ®Google Scholar
• ——— (2004), “A Bayesian Prediction Using the Skew-Gaussian Processes,” Journal of Statistical Planning and Inference, 120, 85–101.
   Web of Science ®Google Scholar
• Mahmoudian, B., and Mohammadzadeh, M. (2014), “A Spatio-Temporal Dynamic Regression Model for Extreme Wind Speeds,” Extremes, 17, 221–245.
   Web of Science ®Google Scholar
• Minozzo, M., and Ferracuti, L. (2012), “On the Existence of Some Skew-Normal Stationary Processes,” Chilean Journal of Statistics, 3, 157–170.
   Google Scholar
• Palacios, M. B., and Steel, M. F. J. (2006), “Non-Gaussian Bayesian Geostatistical Modelling,” Journal of the American Statistical Association, 101, 604–618.
   Web of Science ®Google Scholar
• Roberts, G. O., and Rosenthal, J. S. (2009), “Examples of Adaptive MCMC,” Journal of Computational and Graphical Statistics, 18, 349–367.
   Web of Science ®Google Scholar
• Røislien, J., and Omre, H. (2006), “T-Distributed Random Fields: A Parametric Model for Heavy-Tailed Well-Log Data,” Mathematical Geology, 38, 821–849.
   Google Scholar
• Sahu, S. K., Dey, D. K., and Branco, M. D. (2003), “A New Class of Multivariate Skew Distributions With Applications to Bayesian Regression Models,” Canadian Journal of Statistics, 31, 129–150.
   Web of Science ®Google Scholar
• Schmidt, A. M., Conceição, G., and Moreira, A. (2008), “Investigating the Sensitivity of Gaussian Processes to the Choice of Their Correlation Function and Prior Specifications,” Journal of Statistical Computation and Simulation, 78, 681–699.
   Web of Science ®Google Scholar
• Wadsworth, J. L., Tawn, J. A., and Jonathan, P. (2010), “Accounting for Choice of Measurement Scale in Extreme Value Modeling,” Annals of Applied Statistics, 4, 1558–1578.
   Web of Science ®Google Scholar
• Zareifard, H., and Khaledi, M. J. (2013), “Non-Gaussian Modeling of Spatial Data Using Scale Mixing of a Unified Skew Gaussian Process,” Journal of Multivariate Analysis, 114, 16–28.
   Web of Science ®Google Scholar
• Zhang, H., and El-Shaarawi, A. (2010), “On Spatial Skew-Gaussian Processes and Applications,” Environmetrics, 21, 33–47.
   Web of Science ®Google Scholar