Dynamically Updated Spatially Varying Parameterizations of Hierarchical Bayesian Models for Spatial Data

References

• Akima, H., and Gebhardt, A. (2016), “akima: Interpolation of Irregularly and Regularly Spaced Data,” R package version 0.6-2.
   Google Scholar
• Bakar, K. S., and Sahu, S. K. (2015), “spTimer: Spatio-Temporal Bayesian Modeling Using R,” Journal of Statistical Software, 63, 1–32.
   Web of Science ®Google Scholar
• Bass, M. R., and Sahu, S. K. (2017), “A Comparison of Centring Parameterisations of Gaussian Process-Based Models for Bayesian Computation using MCMC,” Statistics and Computing, 27, 1491–1512.
   Web of Science ®Google Scholar
• Berrocal, V. J., Gelfand, A. E., and Holland, D. M. (2010), “A Spatio-Temporal Downscaler for Output from Numerical Models,” Journal of Agricultural, Biological, and Environmental statistics, 15, 176–197.
   PubMed Web of Science ®Google Scholar
• Besag, J., and Green, P. J. (1993), “Spatial Statistics and Bayesian Computation” (with discussion), Journal of the Royal Statistical Society, Series B, 55, 25–37.
   Google Scholar
• Bivand, R., and Lewin-Koh, N. (2016), “maptools: Tools for Reading and Handling Spatial Objects,” R package version 0.8-39.
   Google Scholar
• Brooks, S. P., and Gelman, A. (1998), “General Methods for Monitoring Convergence of Iterative Simulations,” Journal of Computational and Graphical Statistics, 7, 434–455.
   Web of Science ®Google Scholar
• Cressie, N., and Johannesson, G. (2008), “Fixed Rank Kriging for very Large Spatial Data Sets,” Journal of the Royal Statistical Society, Series B, 70, 209–226.
   Google Scholar
• Finley, A. O., Banerjee, S., and Gelfand, A. E. (2015), “spBayes for Large Univariate and Multivariate Point-Referenced Spatio-Temporal Data Models,” Journal of Statistical Software, 63, 1–28.
   Web of Science ®Google Scholar
• Finley, A. O., Banerjee, S., and MacFarlane, D. W. (2011), “A Hierarchical Model for Quantifying Forest Variables over Large Heterogeneous Landscapes with Uncertain Forest Areas,” Journal of the American Statistical Association, 106, 31–48.
   PubMed Web of Science ®Google Scholar
• Gelfand, A. E., Kim, H.-J., Sirmans, C., and Banerjee, S. (2003), “Spatial Modeling with Spatially Varying Coefficient Processes,” Journal of the American Statistical Association, 98, 387–396.
   Web of Science ®Google Scholar
• Gelfand, A. E., Sahu, S. K., and Carlin, B. P. (1995), “Efficient Parameterisations for Normal Linear Mixed Models,” Biometrika, 82, 479–488.
   Web of Science ®Google Scholar
• Gelfand, A. E., and Smith, A. F. (1990), “Sampling-Based Approaches to Calculating Marginal Densities,” Journal of the American Statistical Association, 85, 398–409.
   Web of Science ®Google Scholar
• Gelman, A., and Rubin, D. B. (1992), “Inference from Iterative Simulation using Multiple Sequences,” Statistical Science, 7, 457–472.
   Google Scholar
• Gneiting, T., Balabdaoui, F., and Raftery, A. E. (2007), “Probabilistic Forecasts, Calibration and Sharpness,” Journal of the Royal Statistical Society, Series B, 69, 243–268.
   Google Scholar
• Hamm, N., Finley, A., Schaap, M., and Stein, A. (2015), “A Spatially Varying Coefficient Model for Mapping PM10 Air Quality at the European Scale,” Atmospheric Environment, 102, 393–405.
   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
• Harville, D. A. (1997), Matrix Algebra from a Statistician’s Perspective, New York: Springer-Verlag.
   Google Scholar
• Huerta, G., Sansó, B., and Stroud, J. R. (2004), “A Spatio-temporal Model for Mexico City ozone Levels,” Journal of the Royal Statistical Society, Series C, 53, 231–248.
   Google Scholar
• Matérn, B. (1986), Spatial Variation (2nd ed.), Berlin: Springer Verlag.
   Google Scholar
• Papaspiliopoulos, O. (2003), “Non-Centered Parameterisations for Data Augmentation and Hierarchical Models with Applications to Inference for Lévy-Based Stochastic Volatility Models,” Ph.D. thesis, University of Lancaster.
   Google Scholar
• Papaspiliopoulos, O., Roberts, G. O., and Sköld, M. (2003), “Non-centered parameterisations for hierarchical models and data augmentation (with discussion),” in Bayesian Statistics 7 (Bernardo, JM and Bayarri, MJ and Berger, JO and Dawid, AP and Heckerman, D and Smith, AFM and West, M): Proceedings of the Seventh Valencia International Meeting, Oxford University Press, USA, pp. 307–326.
   Google Scholar
• Plummer, M., Best, N., Cowles, K., and Vines, K. (2006), “CODA: Convergence Diagnosis and Output Analysis for MCMC,” R News, 6, 7–11.
   Google Scholar
• R Core Team (2016), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Robert, C. O., and Casella, G. (2004), Monte Carlo Statistical Methods” (2nd ed.), New York: Springer-Verlag.
   Google Scholar
• Sahu, S. K., Gelfand, A. E., and Holland, D. M. (2007), “High-Resolution Space–Time Ozone Modeling for Assessing Trends,” Journal of the American Statistical Association, 102, 1221–1234.
   PubMed Web of Science ®Google Scholar
• ——— (2010), “Fusing Point and Areal Level Space–Time Data with Application to Wet Deposition,” Journal of the Royal Statistical Society, Series C, 59, 77–103.
   Google Scholar
• Savage, N., Agnew, P., Davis, L., Ordóñez, C., Thorpe, R., Johnson, C., O’Connor, F., and Dalvi, M. (2013), “Air Quality Modelling using the Met Office Unified Model (AQUM OS24-26): Model Description and Initial Evaluation,” Geoscientific Model Development, 6, 353–372.
   Web of Science ®Google Scholar
• Wheeler, D. C., Páez, A., Spinney, J., and Waller, L. A. (2014), “A Bayesian Approach to Hedonic Price Analysis,” Papers in Regional Science, 93, 663–683.
   Web of Science ®Google Scholar
• Wickham, H. (2009), ggplot2: Elegant Graphics for Data Analysis, New York: Springer-Verlag.
   Google Scholar
• ——— (2017), “tidyr: Easily Tidy Data with ‘spread()’ and ‘gather()’ Functions,” R package version 0.6.1.
   Google Scholar
• Yu, Y., and Meng, X.-L. (2011), “To Center or Not to Center: That is Not the Question: An Ancillarity–Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Efficiency,” Journal of Computational and Graphical Statistics, 20, 531–570.
   Web of Science ®Google Scholar
• Zhang, H. (2004), “Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics,” Journal of the American Statistical Association, 99, 250–261.
   Web of Science ®Google Scholar