Advertisement

A time-dependent PDE regularization to model functional data defined over spatio-temporal domains

  • Eleonora Arnone
  • Laura Azzimonti
  • Fabio Nobile
  • Laura M. Sangalli
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

We propose a method for the analysis of functional data defined over spatio-temporal domains when prior knowledge on the phenomenon under study is available. The model is based on regression with Partial Differential Equations (PDE) penalization. The PDE formalizes the information on the phenomenon and models the regularity of the field in space and time.

Keywords

Functional Data Ordinary Kriging Environ Ecol Stat Partial Differential Equation Stochastic Environ 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aguilera-Morillo, M. C., Durbán, M., Aguilera, A. M.: Prediction of functional data with spatial dependence: a penalized approach. Stochastic Environ Res Risk Assess 31(1): 7–22 (2017)Google Scholar
  2. 2.
    Augustin, N. H., Trenkel, V. M., Wood, S. N., Lorance, P.: Space-time modeling of blue ling for fisheries stock management. Environmetrics 24(2): 109–119 (2013)Google Scholar
  3. 3.
    Azzimonti, L., Nobile, F., Sangalli, L. M., Secchi, P.: Mixed Finite Elements for Spatial Regression with PDE Penalization. SIAM/ASA Journal on Uncertainty Quantification 2(1): 305–335 (2014)Google Scholar
  4. 4.
    Azzimonti, L., Sangalli, L. M., Secchi, P., Domanin, M., Nobile, F.: Blood flow velocity field estimation via spatial regression with PDE penalization. Journal of the American Statistical Association 110(511): 1057–1071 (2015)Google Scholar
  5. 5.
    Bernardi, M. S., Sangalli, L. M., Mazza, G., Ramsay, J. O.: A penalized regression model for spatial functional data with application to the analysis of the production of waste in Venice province. Stochastic Environmental Research and Risk Assessment, 31(1): 23–38, (2017)Google Scholar
  6. 6.
    Caballero, W., Giraldo, R., Mateu, J.: A universal kriging approach for spatial functional data. Stochastic Environ Res Risk Assess 27(7): 1553–1563 (2013)Google Scholar
  7. 7.
    Delicado, P., Giraldo, R., Comas, C., Mateu, J.: Statistics for spatial functional data: some recent contributions. Environmetrics 21(34): 224–239 (2010)Google Scholar
  8. 8.
    Giraldo, R., Delicado, P., Mateu, J.: Ordinary kriging for functionvalued spatial data. Environ Ecol Stat 18(3): 411–426 (2011)Google Scholar
  9. 9.
    Goulard, M., Voltz, M.: Geostatistical interpolation of curves: a case study in soil science. Geostatistics Troía’92, Springer: 805–816 (1993)Google Scholar
  10. 10.
    Ignaccolo, R., Mateu, J., Giraldo, R.: Kriging with external drift for functional data for air quality monitoring. Stochastic Environ Res Risk Assess 28(5): 1171–1186 (2014)Google Scholar
  11. 11.
    Marra, G., Miller, D. L., Zanin, L.: Modelling the spatiotemporal distribution of the incidence of resident foreign population. Statistica Neerlandica 66(2): 133–160 (2012)Google Scholar
  12. 12.
    Mateu, J., Romano, E.: Advances in spatial functional statistics. Stochastic Environ Res Risk Assess 31(1): 1–6 (2017)Google Scholar
  13. 13.
    Menafoglio, A., Secchi, P., Dalla Rosa, M.: A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space. ElectronJ Stat 7: 2209–2240 (2013)Google Scholar
  14. 14.
    Menafoglio, A., Guadagnini, A., Secchi, P.: A kriging approach based on Aitchison geometry for the characterization of particlesize curves in heterogeneous aquifers. Stochastic Environ Res Risk Assess 28(7): 1835–1851 (2014)Google Scholar
  15. 15.
    Nerini, D., Monestiez, P., Manté, C.: Cokriging for spatial functional data. J Multivar Anal 101(2): 409–418 (2010)Google Scholar
  16. 16.
    Ramsay, T.: Spline smoothing over difficult regions. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 54(2): 307–319 (2002)Google Scholar
  17. 17.
    Sangalli, L. M., Ramsay, J. O., Ramsay, T. O.: Spatial spline regression models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 75(4): 681–703 (2013)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Eleonora Arnone
    • 1
  • Laura Azzimonti
    • 2
  • Fabio Nobile
    • 3
  • Laura M. Sangalli
    • 1
  1. 1.MOX - Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.IDSIA - Department of Innovative TechnologiesUniversitá della Svizzera Italiana Galleria 1LuganoSwitzerland
  3. 3.MATHICSE-CSQI, École Polytechnique Fédérale de LausanneLausanneSwitzerland

Personalised recommendations