Wombling

In statistics, Wombling is any of a number of techniques used for identifying zones of rapid change, typically in some quantity as it varies across some geographical or Euclidean space. It is named for statistician William H. Womble who published an article on the Differential Systematics in Science to highlight the importance of studying rates of change in genetics.

In modern statistics, wombling has been largely developed by statisticians Sudipto Banerjee and Alan E. Gelfand as a methodology to infer the rates of change at points on spatial random fields along curves or boundaries. Wombling has also been applied to geographic maps, especially in public health research, to model or detect whether administrative boundaries represent zones of rapid change in health outcomes. This line of work has been formalized also as multiple testing problems for neighboring spatial effects. Bayesian wombling can be implemented using the R package nimblewomble available from CRAN.

The technique may be applied to gene frequency in a population of organisms, and to evolution of language.

References

• William H. Womble 1951. "Differential Systematics". Science vol 114, No. 2961, p315–322. doi:10.1126/science.114.2961.315
• Banerjee, S. and Gelfand, A.E. (2006) "Bayesian Wombling: Curvilinear Gradient Assessment Under Spatial Process Models", Journal of the American Statistical Association, 101(476), 1487–1501. doi:10.1198/016214506000000041 Available Softtware: CRAN package
• Banerjee, S. (2010) "Spatial Gradients and Wombling", "Handbook of Spatial Statistics", Chapter 31, 18 pages.
• Fitzpatrick M.C., Preisser E.L., Porter A., Elkinton J., Waller L.A., Carlin B.P. and Ellison A.E. (2010) "Ecological boundary detection using Bayesian areal wombling", Ecology 91:3448–3455 doi:10.1890/10-0807.1
• Liang, S., Banerjee, S. and Carlin, B.P. (2009) "Bayesian Wombling for Spatial Point Processes", Biometrics, 65 (11), 1243–1253 doi:10.1111/j.1541-0420.2009.01203.x
• Ma, H. and Carlin, B.P. (2007) "Bayesian Multivariate Areal Wombling for Multiple Disease Boundary Analysis", Bayesian Analysis, 2 (2), 281–302
• 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
• Quick, H., Banerjee, S. and Carlin, B.P. (2013). "Modeling temporal gradients in regionally aggregated California asthma hospitalization data" Annals of Applied Statistics, 7(1), 154–176. doi:10.1214/12-AOAS600
• Halder, A., Banerjee, S. and Dey, D. K. "Bayesian modeling with spatial curvature processes." Journal of the American Statistical Association (2023): 1-13. doi:10.1080/01621459.2023.2177166 Available Software: Git
• Halder, A., Li, D. and Banerjee, S.. "Bayesian spatiotemporal wombling." Journal of the American Statistical Association(2026): 1–28. doi:10.1080/01621459.2026.2700798 Available Software: Git
• Gao, L., Banerjee, S. and Ritz, B. "Spatial Difference Boundary Detection for Multiple Outcomes Using Bayesian Disease Mapping." Biostatistics (journal) (2023): 922–944 doi:10.1093/biostatistics/kxac013.
• Wu, K. and Banerjee, S. (2025) "Assessing spatial disparities: A Bayesian linear regression approach." Biostatistics (journal) 26(1) kxaf048 doi:10.1093/biostatistics/kxaf048.