Advertisement

Dealing with Spatiotemporal Heterogeneity: The Generalized BME Model

  • Hwa-Lung YuEmail author
  • George Christakos
  • Patrick Bogaert
Chapter
Part of the Advances in Spatial Science book series (ADVSPATIAL)

Abstract

Geographical studies involving natural systems and their attributes (e.g., environmental processes, land use parameters, human exposure indicators, disease variables, and financial indexes) often need to quantitatively assess spatiotemporal dependence and generate informative maps of the attributes across space-time. These are important, indeed, goals of spatiotemporal systems modelling and data analysis introduced in a modern statistical framework by Christakos (1990, 1991a,b, 1992). Subsequent works include Goodall and Mardia (1994), Haas (1995), Bogaert (1996), Christakos and Hristopulos (1998), and Kyriakidis and Journel (1999). Among the more recent developments one should notice the works of Serre et al. (2003), Kolovos et al. (2002, 2004), Douaik et al. (2004), Christakos et al. (2002, 2005), Stein (2005), Law et al. (2006), Porcu et al. (2006, 2008), Yu et al. (2007a–c), Renshaw et al. (2008), and Ruiz-Medina et al. (2008a,b).

Keywords

Hard Data Simulated Field Soft Information Soft Data Epistematics Knowledge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Partial support for this work was provided by a grant from the California Air Resources Board, USA (Grant No. 55245A).

References

  1. Bogaert B (1996) Comparison of kriging techniques in a space-time context. Math Geol 28:73–86CrossRefGoogle Scholar
  2. Christakos G (1990) Random Field modelling and its applications in stochastic data processing. PhD Thesis, Applied Sciences Division, Harvard University, Cambridge, MAGoogle Scholar
  3. Christakos G (1991a) On certain classes of spatiotemporal random fields with application to space-time data processing. IEEE T Syst Man Cyb 21:861–875CrossRefGoogle Scholar
  4. Christakos G (1991b) Some applications of the BME concept in geostatistics. Fund Theories Phy: 215–229, Kluwer, Amsterdam, The NetherlandsGoogle Scholar
  5. Christakos G (1992) Random field models in earth sciences. Academic, San Diego, CA. Also, Dover Publ. 2005Google Scholar
  6. Christakos G (2000) Modern spatiotemporal geostatistics. Oxford University Press, New York, NYGoogle Scholar
  7. Christakos G (2002) On the assimilation of uncertain physical knowledge bases: Bayesian and non-Bayesian techniques. Adv Water Resour 25:1257–1274CrossRefGoogle Scholar
  8. Christakos G (2008) Bayesian maximum entropy. In: Kanevski M (ed.) Advanced mapping of environmental data: geostatistics, machine learning, and Bayesian maximum entropy. Wiley, New York, NY, pp 247–306Google Scholar
  9. Christakos G, Bogaert P (1996) Spatiotemporal analysis of spring water ion processes derived from measurements at the Dyle Basin in Belgium. IEEE Trans Geosci Remote Sens 34:626–642CrossRefGoogle Scholar
  10. Christakos G, Bogaert P, Serre ML (2002) Temporal GIS. Springer, New York, with CD-ROMGoogle Scholar
  11. Christakos G, Hristopulos DT (1998) Spatiotemporal environmental health modelling: a Tractatus Stochasticus. Kluwer, BostonGoogle Scholar
  12. Christakos G, Olea RA, Serre ML, Yu HL, Wang LL (2005) Interdisciplinary public health reasoning and epidemic modelling: the case of black death. Springer, New YorkGoogle Scholar
  13. Christakos G, Raghu VR (1996) Dynamic stochastic estimation of physical variables. Mathematical Geology 28:341–365CrossRefGoogle Scholar
  14. Christakos G, Thesing GA (1993) The Intrinsic Random-Field Model in the Study of Sulfate Deposition Processes. Atmos Environ Gen Top 27:1521–1540CrossRefGoogle Scholar
  15. Douaik A, van Meirvenne M, Toth T, Serre ML (2004) Space-time mapping of soil salinity using probabilistic BME. Stoch Environ Res Risk Assess 18:219–227CrossRefGoogle Scholar
  16. Goodall C, Mardia KV (1994) Challenges in multivariate spatio-temporal modeling. In: Proceedings of the XVIIth International Biometric Conference, 1–17, Hamilton, Ontario, Canada, 8–12 August 1994Google Scholar
  17. Gupta AK, Nagar DK (2000) Matrix variate distributions. Chapman & Hall, Boca Raton, FLGoogle Scholar
  18. Haas TC (1995) Local prediction of spatio-temporal process with an application to wet sulfate deposition. J Am Stat Assoc 90:1189–1199CrossRefGoogle Scholar
  19. Kolovos A, Christakos G, Serre ML, Miller CT (2002) Computational BME solution of a stochastic advection-reaction equation in the light of site-specific information. Water Resour Res 38:1318–1334CrossRefGoogle Scholar
  20. Kitanidis PK (1983) Statistical estimation of polynomial generalized covariance functions and hydrologic applications. Water Resour Res 19:909–921CrossRefGoogle Scholar
  21. Kitanidis PK, Shen KF (1996) Geostatistical interpolation of chemical concentration. Adv Water Resour 19:369–378CrossRefGoogle Scholar
  22. Kolovos A, Christakos G, Hristopulos DT, Serre ML (2004) Methods for generating non-separable spatiotemporal covariance models with potential environmental applications. Adv Water Resour 27:815–830CrossRefGoogle Scholar
  23. Kolovos A, Yu HL, Christakos G (2006) SEKS-GUI v.0.6 user manual. Department of Geography, San Diego State University, San Diego, CAGoogle Scholar
  24. Kyriakidis PC, Journel AG (1999) Geostatistical space-time models: a review. Math Geol 31:651–684CrossRefGoogle Scholar
  25. Law DC, Bernstein K, Serre ML, Schumacher CM, Leone PA, Zenilman WC Miller, Rompalo AM (2006) Modelling an early syphilis outbreak through space and time using the bayesian maximum entropy approach. Ann Epidemiol 16:797–804CrossRefGoogle Scholar
  26. PardoIguzquiza E (1997) GCINFE: a computer program for inference of polynomial generalized covariance functions. Comput Geosci 23:163–174CrossRefGoogle Scholar
  27. Porcu E, Gregori P, Mateu J (2006) Nonseparable stationary anisotropic space-time covariance functions. Stoch Environ Res Risk Assess 21:113–122CrossRefGoogle Scholar
  28. Porcu E, Mateu J, Saura F (2008) New classes of covariance and spectral density functions for spatio-temporal modelling. Stoch Environ Res Risk Assess 22:65–79CrossRefGoogle Scholar
  29. Renshaw E, Comas C, Mateu J (2008) Analysis of forest thinning strategies through the development of space-time growth-interaction simulation models. Stoch Environ Res Risk Assess. doi:10.1007/s00477–008–0214-xGoogle Scholar
  30. Ruiz-Medina MD, Angulo JM, Anh VV (2008a) Spatiotemporal statistical analysis of influenza mortality risk in the State of California during the period 1997–2001. Stoch Environ Res Risk Assess 22:15–25CrossRefGoogle Scholar
  31. Ruiz-Medina MD, Angulo JM, Anh VV (2008b) Multifractality in space–time statistical models. Stoch Environ Res Risk Assess 22:81–86CrossRefGoogle Scholar
  32. Serre ML, Kolovos A, Christakos G, Modis K (2003) An application of the holistochastic human exposure methodology to naturally occurring Arsenic in Bangladesh drinking water. Risk Anal 23:515–528CrossRefGoogle Scholar
  33. Stein A (1998) Analysis of space-time variability in agriculture and the environment with geostatistics. Statistica Neerlandica 52:18–41CrossRefGoogle Scholar
  34. Stein ML (2005) Space-time covariance functions. J Am Stat Assoc 100:310–321CrossRefGoogle Scholar
  35. Vyas VM, Christakos G (1997) Spatiotemporal analysis and mapping of sulfate deposition data over eastern USA. Atmos Environ 31:3623–3633CrossRefGoogle Scholar
  36. Yu HL (2005) Development and implementation of knowledge synthesis methods for stochastic natural systems. PhD Thesis, University of North Carolina at Chapel Hill, Department of Environmental Sciences and Engineering, Chapel Hill, NC, USAGoogle Scholar
  37. Yu HL, Christakos G (2006) Spatiotemporal modelling and mapping of the bubonic plague epidemic in India. Int J Health Geogr 5 (Internet Journal)Google Scholar
  38. Yu HL, Kolovos A, Christakos G, Chen JC, Warmerdam S, Dev B (2007a) Interactive spatiotemporal modelling of health systems: The SEKS-GUI framework. J Stoch Environ Res Risk Assess – Special Issue on “Medical Geography as a Science of Interdisciplinary Knowledge Synthesis under Conditions of Uncertainty,” Griffith DA, Christakos G (eds) 21:555–572Google Scholar
  39. Yu HL, Christakos G, Modis K, Papantonopoulos G (2007b) A composite solution method for physical equations and its application in the Nea Kessani geothermal field (Greece). J Geophys Res B Solid Earth Planets 112:B06104. doi:10.1029/2006JB004900CrossRefGoogle Scholar
  40. Yu HL, Christakos G (2009) Generalized BME processing and imaging of heterogeneous space-time data. Working paper available from the authorsGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Bioenvironmental Systems EngineeringNational Taiwan UniversityTaipeiTaiwan, R.O.C.

Personalised recommendations