Bayesian Modeling with Spatial Curvature Processes

References

• Abramowitz, M., Stegun, I. A., and Romer, R. H. (1988), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Washington, DC: United States. Government Printing Office.
   Google Scholar
• Adler, R. J. (1981), The Geometry of Random Fields, Philadelphia, PA: SIAM.
   Google Scholar
• Albering, H. J., Van Leusen, S. M., Moonen, E., Hoogewerff, J. A., and Kleinjans, J. (1999), “Human Health Risk Assessment: A Case Study Involving Heavy Metal Soil Contamination After The Flooding of The River Meuse During The Winter Of 1993-1994,” Environmental Health Perspectives, 107, 37–43. DOI: 10.1289/ehp.9910737.
   PubMed Web of Science ®Google Scholar
• Banerjee, S. (2010), “Spatial Gradients and Wombling,” in Handbook of Spatial Statistics, eds. A. E. Gelfand, P. Diggle, P. Guttorp, and M. Fuentes, 559–574, Boca Raton, FL: Taylor and Francis/CRC.
   Google Scholar
• Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2014), Hierarchical Modeling and Analysis for Spatial Data, Boca Raton, FL: CRC Press.
   Google Scholar
• Banerjee, S., and Gelfand, A. (2003), “On Smoothness Properties of Spatial Processes,” Journal of Multivariate Analysis, 84, 85–100. DOI: 10.1016/S0047-259X(02)00016-7.
   Web of Science ®Google Scholar
• Banerjee, S., and Gelfand, A. E. (2006), “Bayesian Wombling: Curvilinear Gradient Assessment Under Spatial Process Models,” Journal of the American Statistical Association, 101, 1487–1501. DOI: 10.1198/016214506000000041.
   PubMed Web of Science ®Google Scholar
• Banerjee, S., Gelfand, A. E., and Sirmans, C. (2003), “Directional Rates of Change Under Spatial Process Models,” Journal of the American Statistical Association, 98, 946–954. DOI: 10.1198/C16214503000000909.
   Web of Science ®Google Scholar
• Burrough, P. A., McDonnell, R. A., and Lloyd, C. D. (2015), Principles of Geographical Information Systems, Oxford: Oxford University Press.
   Google Scholar
• Chen, M.-H., and Shao, Q.-M. (1999), “Monte Carlo Estimation of Bayesian Credible and HPD Intervals,” Journal of Computational and Graphical Statistics, 8, 69–92. DOI: 10.2307/1390921.
   Web of Science ®Google Scholar
• Chiu, S. N., Stoyan, D., Kendall, W. S., and Mecke, J. (2013), Stochastic Geometry and Its Applications, Chichester: Wiley.
   Google Scholar
• Do Carmo, M. P. (2016), Differential Geometry of Curves and Surfaces: Revised and Updated (2nd ed.), Mineola, NY: Courier Dover Publications.
   Google Scholar
• Dryden, I. L., and Mardia, K. V. (2016), Statistical Shape Analysis: With Applications In R (Vol. 995), Chichester: Wiley.
   Google Scholar
• Elliot, P., Wakefield, J. C., Best, N. G., and Briggs, D. J. (2000), Spatial Epidemiology: Methods and Applications, Oxford: Oxford University Press.
   Google Scholar
• Fitzpatrick, M. C., Preisser, E. L., Porter, A., Elkinton, J., Waller, L. A., Carlin, B. P., and Ellison, A. M. (2010), “Ecological Boundary Detection Using Bayesian Areal Wombling,” Ecology, 91, 3448–3455. DOI: 10.1890/10-0807.1.
   PubMed Web of Science ®Google Scholar
• Gallier, J., and Gallier, J. H. (2000), Curves and Surfaces in Geometric Modeling: Theory and Algorithms, San Francisco, CA: Morgan Kaufmann.
   Google Scholar
• Gao, L., Banerjee, S., and Ritz, B. (2022), “Spatial Difference Boundary Detection for Multiple Outcomes Using Bayesian Disease Mapping,” Biostatistics, kxac013. DOI: 10.1093/biostatistics/kxac013.
   Google Scholar
• Gleyze, J. F., Bacro, J. N., and Allard, D. (2001), “Detecting Regions of Abrupt Change: Wombling Procedure and Statistical Significance,” in geoENV III—Geostatistics for Environmental Applications, eds. P. Monestiez, D. Allard and R. Froidevaux, pp. 311–322, Dordrecht: Springer.
   Google Scholar
• Greenwood, J., (1984), “A Unified Theory of Surface Roughness,” Proceedings of the Royal Society of London, Series A, 393, 133–157.
   Web of Science ®Google Scholar
• Haining, R. (1993), Spatial Data Analysis in the Social and Environmental Sciences, Cambridge: Cambridge University Press.
   Google Scholar
• Harrison Jr, D., and Rubinfeld, D. L. (1978), “Hedonic Housing Prices and the Demand for Clean Air,” Journal of Environmental Economics and Management, 5, 81–102. DOI: 10.1016/0095-0696(78)90006-2.
   Web of Science ®Google Scholar
• Heaton, M. J. (2014), “Wombling Analysis of Childhood Tumor Rates in Florida,” Statistics and Public Policy, 1, 60–67. DOI: 10.1080/2330443X.2014.913512.
   Google Scholar
• Heaton, M. J., Datta, A., Finley, A. O., Furrer, R., Guinness, J., Guhaniyogi, R., Gerber, F., Gramacy, R. B., Hammerling, D., Katzfuss, M. et al. (2019), “A Case Study Competition Among Methods for Analyzing Large Spatial Data,” Journal of Agricultural, Biological and Environmental Statistics, 24, 398–425. DOI: 10.1007/s13253-018-00348-w.
   PubMed Web of Science ®Google Scholar
• Hu, L., He, S., Han, Z., Xiao, H., Su, S., Weng, M., and Cai, Z. (2019), “Monitoring Housing Rental Prices Based on Social Media: An Integrated Approach of Machine-Learning Algorithms and Hedonic Modeling to Inform Equitable Housing Policies,” Land Use Policy, 82, 657–673. DOI: 10.1016/j.landusepol.2018.12.030.
   Web of Science ®Google Scholar
• Jones, C. B. (2014), Geographical Information Systems and Computer Cartography, London: Routledge.
   Google Scholar
• Kent, J. T. (1989), “Continuity Properties for Random Fields,” The Annals of Probability, 17, 1432–1440. DOI: 10.1214/aop/1176991163.
   Web of Science ®Google Scholar
• Kent, J. T., Mardia, K. V., and Taylor, C. C. (2008), “Modelling Strategies for Bivariate Circular Data,” in Proceedings of the Leeds Annual Statistical Research Conference, The Art and Science of Statistical Bioinformatics, pp. 70–73, Leeds: Leeds University Press.
   Google Scholar
• Law, A. M., Kelton, W. D., and Kelton, W. D. (2000), Simulation Modeling and Analysis (Vol. 3), New York: McGraw-Hill.
   Google Scholar
• Lawson, A. B. (2013), Statistical Methods in Spatial Epidemiology, Chichester: Wiley.
   Google Scholar
• Leenaers, H., Schouten, C., and Rang, M. (1988), “Variability of the Metal Content of Flood Deposits,” Environmental Geology and Water Sciences, 11, 95–106. DOI: 10.1007/BF02587768.
   Web of Science ®Google Scholar
• LeSage, J., and Pace, R. K. (2009), Introduction to Spatial Econometrics, Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Li, P., Banerjee, S., Hanson, T. A., and McBean, A. M. (2015), “Bayesian Models for Detecting Difference Boundaries in Areal Data,” Statistica Sinica, 25, 385–402.
   PubMed Web of Science ®Google Scholar
• Liang, S., Banerjee, S., and Carlin, B. P. (2009), “Bayesian Wombling for Spatial Point Processes,” Biometrics, 65, 1243–1253. DOI: 10.1111/j.1541-0420.2009.01203.x.
   PubMed Web of Science ®Google Scholar
• Lu, H., and Carlin, B. P. (2005), “Bayesian Areal Wombling for Geographical Boundary Analysis,” Geographical Analysis, 37, 265–285. DOI: 10.1111/j.1538-4632.2005.00624.x.
   Web of Science ®Google Scholar
• Magnus, J. R., and Neudecker, H. (1980), “The Elimination Matrix: Some Lemmas and Applications,” SIAM Journal on Algebraic Discrete Methods, 1, 422–449. DOI: 10.1137/0601049.
   Google Scholar
• Majumdar, A., Munneke, H. J., Gelfand, A. E., Banerjee, S., and Sirmans, C. (2006), “Gradients in Spatial Response Surfaces With Application to Urban Land Values,” Journal of Business & Economic Statistics, 24, 77–90. DOI: 10.1198/073500105000000162.
   Web of Science ®Google Scholar
• Mardia, K., Kent, J., Goodall, C., and Little, J. (1996), “Kriging and Splines with Derivative Information,” Biometrika, 83, 207–221. DOI: 10.1093/biomet/83.1.207.
   Web of Science ®Google Scholar
• Matérn, B., (2013), Spatial Variation (Vol. 36), New York: Springer.
   Google Scholar
• Morris, M. D., Mitchell, T. J., and Ylvisaker, D. (1993), “Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction,” Technometrics, 35, 243–255. DOI: 10.1080/00401706.1993.10485320.
   Web of Science ®Google Scholar
• Pebesma, E., Bivand, R., Pebesma, M. E., RColorBrewer, S., and Collate, A. (2012), “Package ‘sp’,” The Comprehensive R Archive Network.
   Google Scholar
• Plant, R. E. (2018), Spatial Data Analysis in Ecology and Agriculture Using R, Boca Raton, FL: CRC Press.
   Google Scholar
• Plummer, M., Best, N., Cowles, K., and Vines, K. (2015), “Package ‘coda’,” Available at http://cran.r-project.org/web/packages/coda/coda.pdf, accessed January 25, 2015.
   Google Scholar
• Qu, K., Bradley, J. R., and Niu, X. (2021), “Boundary Detection Using a Bayesian Hierarchical Model for Multiscale Spatial Data,” Technometrics, 63, 64–76. DOI: 10.1080/00401706.2019.1677268.
   Web of Science ®Google Scholar
• Quick, H., Banerjee, S., and Carlin, B. P. (2015), “Bayesian Modeling and Analysis for Gradients in Spatiotemporal Processes,” Biometrics, 71, 575–584. DOI: 10.1111/biom.12305.
   PubMed Web of Science ®Google Scholar
• Rudin, W. (1976), Principles of Mathematical Analysis (Vol. 3), New York: McGraw-Hill.
   Google Scholar
• Santner, T. J., Williams, B. J., Notz, W. I., and Williams, B. J. (2003), The Design and Analysis of Computer Experiments (Vol. 1), New York: Springer.
   Google Scholar
• Schabenberger, O., and Gotway, C. A. (2017), Statistical Methods for Spatial Data Analysis, Boca Raton, FL: CRC Press.
   Google Scholar
• Schnare, A. B., and Struyk, R. J. (1976), “Segmentation in Urban Housing Markets,” Journal of Urban Economics, 3, 146–166. DOI: 10.1016/0094-1190(76)90050-4.
   Web of Science ®Google Scholar
• Spivak, M. (1999), A Comprehensive Introduction to Differential Geometry, in A Comprehensive Introduction to Differential Geometry (Vols. 1–5), Houston, TX: Publish or Perish Inc.
   Google Scholar
• Stein, M. L. (1999), Interpolation of Spatial Data: Some Theory for Kriging, New York: Springer.
   Google Scholar
• Stevens, K. A. (1981), “The Visual Interpretation of Surface Contours,” Artificial Intelligence, 17, 47–73. DOI: 10.1016/0004-3702(81)90020-5.
   Web of Science ®Google Scholar
• Terres, M. A., and Gelfand, A. E. (2015), “Using Spatial Gradient Analysis to Clarify Species Distributions With Application to South African Protea,” Journal of Geographical Systems, 17, 227–247. DOI: 10.1007/s10109-015-0215-5.
   Web of Science ®Google Scholar
• Terres, M. A., and Gelfand, A. E. (2016), “Spatial Process Gradients and their Use in Sensitivity Analysis for Environmental Processes,” Journal of Statistical Planning and Inference, 168, 106–119. DOI: 10.1016/j.jspi.2015.07.003.
   Web of Science ®Google Scholar
• Vaughan, L. (2018), Mapping Society: The Spatial Dimensions of Social Cartography, London: UCL Press.
   Google Scholar
• Waller, L. A., and Gotway, C. A. (2004), Applied Spatial Statistics for Public Health Data (Vol. 368), Hoboken, NJ: Wiley.
   Google Scholar
• Wang, F., Bhattacharya, A., and Gelfand, A. E. (2018), “Process Modeling for Slope and Aspect with Application to Elevation Data Maps,” Test, 27, 749–772. DOI: 10.1007/s11749-018-0619-x.
   Web of Science ®Google Scholar
• Wang, X., and Berger, J. O. (2016), “Estimating Shape Constrained Functions Using Gaussian Processes,” SIAM/ASA Journal on Uncertainty Quantification, 4, 1–25. DOI: 10.1137/140955033.
   Web of Science ®Google Scholar
• Webster, R., and Oliver, M. A. (2007), Geostatistics for Environmental Scientists, Chichester: Wiley.
   Google Scholar
• Williams, C. K., and Rasmussen, C. E. (2006), Gaussian Processes for Machine Learning (Vol. 2), Cambridge, MA: MIT Press.
   Google Scholar
• Winkler, G. (2003), Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Vol. 27), Berlin: Springer.
   Google Scholar
• Wise, S., and Craglia, M. (2007), GIS and Evidence-Based Policy Making, Boca Raton, FL: CRC Press.
   Google Scholar
• Womble, W. H. (1951), “Differential Systematics,” Science, 114, 315–322. DOI: 10.1126/science.114.2961.315.
   PubMed Web of Science ®Google Scholar