Skip to main content
SpringerLink
Log in

Stochastische Modelle für Raum-Zeit-Daten

  • Chapter
Bevölkerungsentwicklung in Zeit und Raum

  • 1194 Accesses

Zusammenfassung

Statistische Bestandsdaten wie Bevölkerungszahlen und Ereignisdaten wie Geburtenzahlen beziehen sich auf einen bestimmten Ort und einen bestimmten Zeitpunkt oder Zeitraum. Die Methoden der inferenzstatistischen Analyse solcher Raum-Zeit-Daten lassen sich einbetten in das statistische Spezialgebiet der Raum-Zeitlichen Datenanalyse, die als Kombination der Räumlichen Statistik mit der Zeitreihenanalyse angesehen werden kann. Die Theorie der Zeitreihenanalyse entwickelte sich in der Mitte des 20. Jahrhunderts, bevor vor allem in den 80er Jahren die Räumliche Datenanalyse intensiv erforscht und ausgearbeitet wurde. Aufbauend auf den hier gewonnenen Erkenntnissen entstand der Bedarf, diese beiden Modellsituationen im Anschluss daran miteinander zu verbinden, so dass die 90er Jahre teilweise als das „Zeitalter der Raum-Zeitlichen Statistik“ bezeichnet werden. Man betrachtet hier also Folgen von Zufallsvariablen mit räumlicher und zeitlicher Indizierung, die einen sogenannten raum-zeitlichen Stochastischen Prozess bilden.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  • Abraham, Bovas (1983): The exact likelihood function for a space-time model. Metrika 30, S.239-243.

    Article  Google Scholar 

  • Aroian, Leo A. (1980): Time series in m dimensions – definitions, problems, and prospects. Communications in Statistics – Simulation and Computation B 9, S.453-465.

    Article  Google Scholar 

  • Bennett, Robert John (1979): Spatial Time Series. London.

    Google Scholar 

  • Berke, Olaf (1993): Statistische Analyse von räumlich und zeitlich verteilten forsthydrologischen Daten. Diplomarbeit Universität Dortmund.

    Google Scholar 

  • Berke, Olaf (1998): Über die statistische On-line-Prädiktion von Umweltmonitoringdaten im Rahmen von dynamischen linearen Raum-Zeit-Modellen. Dissertation Universität Dortmund.

    Google Scholar 

  • Berliner, L.Mark/Wikle, Christopher K../Milliff, Ralph F.(1999): Multiresolution wavelet analyses in hierarchical Bayesian turbulence models. In: P.Müller und B.Vidakovic (Hrsg.), Bayesian Inference in Wavelet-Based Models – Lecture Notes in Statistics 141, S.341-359. New York.

    Google Scholar 

  • Berliner, L.Mark/Wikle, Christopher K../Cressie, Noel A.C. (2000): Long-lead prediction of Pacific SSTs via Bayesian dynamic modeling. Journal of Climate 13, S. 3953-3968.

    Article  Google Scholar 

  • Bogaert, Patrick (1996): Comparison of kriging techniques in a space-time context. Mathematical Geology 28 (1), S. 73-86.

    Article  Google Scholar 

  • Bogaert, Patrick/Christakos, George (1997): Spatiotemporal analysis and processing of thermometric data over Belgium. Journal of Geographic Research. – Atmospheres 102 (D22), 25831-25846.

    Article  Google Scholar 

  • Buxton, Bruce E./Pate, Alan D. (1994): Joint temporal-spatial modeling of concentrations of hazardous pollutants in urban air. In: R. Dimitrakopoulos (Hrsg.), Geostatistics for the Next Century, S.75-87. Dordrecht.

    Google Scholar 

  • Cane, Mark A./Kaplan, Alexey /Miller, Robert N./Tang, Benyang/ Hackert,Eric C./Busalacchi, Antonio J. (1996): Mapping tropical Pacific sea level – data assimilation via a reduced state space Kalman filter. Journal of Geophysical Research 101 (C 10), 22599-22617.

    Article  Google Scholar 

  • Cliff, Andrew David/Hagget, Petder/Ord, J. Keith/ /Bassett, Keith A. /Davies, Richard B. (1975): Elements of Spatial Structure – A Quantitative Approach. Cambridge.

    Google Scholar 

  • Cohen, Albert/Jones, R. Howard (1969): Regression on a random field. Journal of the American Statistical Association 64, S.1172-1182.

    Article  Google Scholar 

  • Cressie, Noel A.C. (1993): Statistics for Spatial Data, Revised Edition. New York.

    Google Scholar 

  • Cressie, Noel A.C. (1994): Comment on M.S.Handcock and J.R.Wallis – An aproach to statistical spatial-temporal modeling of meteorological fields. Journal of the American Statistical Association 89, S.379-382.

    Article  Google Scholar 

  • Cressie, Noel A.C. /Majure, James J. (1997): Spatio-temporal statistical modeling of livestock waste in streams. Journal of Agricultural, Biological, and Environmental Statistics 2, S.24-47.

    Article  Google Scholar 

  • Cressie, Noel A.C. /Wikle, Christopher K. (1998): Comment on K.V.Mardia, C.R.Goodall, E.J.Redfern and F.J.Alonso – The kriged Kalman filter. Test 7(2), S.257-264.

    Google Scholar 

  • Cressie, Noel A.C. /Huang, Hsin-Cheng (1999): Classes of nonseparable, spatio-temporal stationary covariance functions. Journal of the American Statistical Association 94, S.1330-1340.

    Article  Google Scholar 

  • DeCesare, Luigi/Myers,Donald E./ Posa ,D. (1997): Spatio-temporal modeling of SO 2 in Milan district. In: E.Y. Baaffi und N.A. Schofield (Hrsg.), Geostatistics Wollongong ’96 (2), S. 1031-1042. Dordrecht.

    Google Scholar 

  • DeIaco, ,S./ Myers, Donald E./ Posa,D. (2002): Nonseparable space-time covariance models – Some parametric families. Mathematical Geology 34 (1), S. 23-42.

    Article  Google Scholar 

  • Fried, Roland (1999): Räumlich-zeitliche Modellierung der Kohlenstoffkonzentration im Waldbodensickerwasser zur Untersuchung der Hypothese der Humusdisintegration. Berlin.

    Google Scholar 

  • Gelman, Andrew/Carlin, John B./ Stern, Hal S./Rubin, Donald B. (1995): Baysian Data Analysis. London.

    Google Scholar 

  • Gerß, Joachim Werner Otto (1998): Statistische Analyse von Raum-Zeit-Daten aus der Limnologie – Untersuchung aktiver Vertikalbewegungen von Schwefelpurpurbakterien in ihrer natürlichen Umgebung. Diplomarbeit Universität Dortmund.

    Google Scholar 

  • Gerß, Joachim Werner Otto (2004): Prädiktion der Ozeantemperatur im räumlichen und zeitlichen Verlauf mit Hilfe dynamischer linearer Modelle. Berlin.

    Google Scholar 

  • Ghil, Michael/Cohn, Stephen E./Tavantzis, John/Bube, K./ Isaacson , Eugene(1981): Applications of estimation theory to numerical weather prediction. In: L. Bengtsson, M. Ghil und E. Källén (Hrsg.), Dynamic Meteorology – Data Assilmilation Methods, S. 139-224. New York.

    Google Scholar 

  • Gilks, Walter R./ Richardson, Sylvia/Spiegelhalter, David J. (1996): Markov Chain Monte Carlo in Practice. London.

    Google Scholar 

  • Gneiting,, Tilmann (2002): Nonseparable, stationary covariance functions for space-time data. Journal of the American Statistical Association 97, S.590-690.

    Article  Google Scholar 

  • Goodall, Colin R. /Phelan, M.J.P. (1990): Edge-preserving smoothing and the assessment of point process models for GATE rainfall fields. In: N.U. Prabhu und I.V. Basawar (Hrsg.), Statistical Inference in Stochastic Processes, S.35-66. New York.

    Google Scholar 

  • Goodall, Colin R. /Mardia, Kantilal Vardichand (1994): Challenges in Multivariate Spatio-Temporal Modeling. Proceedings of the XVII th International Biometric Conference. Hamilton (Ontario, Canada).

    Google Scholar 

  • Green, Peter J./ Titterington, D. Michael (1988): Recursive methods in image processing. Bulletin of the International Statistical Institute 52 (4), S.51-67.

    Google Scholar 

  • Guttorp, Peter/Sampson, Paul D. (1994): Methods for estimating heterogeneous spatial covariance functions with environmental applications. In: G.P. Patil und C.R. Rao (Hrsg.), Environmental Statistics – Handbook of Statistics 12, S.661-689. Amsterdam.

    Google Scholar 

  • Guttorp, Peter /Meiring,Wendy/Sampson, Paul D. (1994): A space-time analysis of ground-level ozone data. Environmetrics 5, S.241-254.

    Article  Google Scholar 

  • Handcock, Mark S./Wallis, James R. (1994): An approach to statistical spatial- temporal modeling of meteorological fields. Journal of the American Statistical Association 89, S.368-390.

    Article  Google Scholar 

  • Haslett, John (1989): Space time modelling in meteorology – A review. Bulletin of the International Statistical Institute 51 (1), S. 229-246.

    Google Scholar 

  • Haslett, John/Raftery, Adrian E. (1989): Space-time modelling with long-memory dependence – assessing Ireland’s wind power resource. Applied Statistics 38, S.1-50.

    Article  Google Scholar 

  • Heuvelink, Gerard B.M./Musters, P./Pebesma, Edzer J. (1997): Spatio-temporal kriging of soil water content. In: E.Y. Baaffi und N.A.Schofield (Hrsg.), Geostatistics Wollongong `96 (2), S.1020-1030. Dordrecht.

    Google Scholar 

  • Higdon, David (1998): A process-convolution approach to modelling temperatures in the north Atlantic Ocean. Environmental and Ecological Statistics 5, S. 173-190.

    Article  Google Scholar 

  • Huang, Hsin-Cheng/Cressie, Noel A.C. (1996): Spatio-temporal prediction of snow water equivalent using the Kalman filter. Computational Statistics and Data Analysis 22, S.159-175.

    Article  Google Scholar 

  • Kappler, Martin (1999): Analyse von Niederschlagsdaten im Rahmen eines Bayes-Ansatzes mit Hilfe von Gibbs-Sampling. Diplomarbeit Universität Dortmund.

    Google Scholar 

  • Krajewski, Pawel/Molinska, A/ Molinski, K. (1996): Elliptical anisotropy in practice – A study of air monitoring data. Environmetrics 7, S.291-298.

    Article  Google Scholar 

  • Kyriakidis, Phaedon C./Journel, André G. (1999): Geostatistical space-time models – A review. Mathematical Geology 31 (6), S.651-684.

    Article  Google Scholar 

  • Loader, Catherine/Switzer, Paul (1992): Spatial covariance estimating for monitoring data. In: A.T. Walden und P. Guttorp (Hrsg.), Statistics in Environmental and Earth Sciences, S.52-70. London.

    Google Scholar 

  • Magnus, Jan R./Neudecker, Heinz (1988) : Matrix Differential Calculus with Applications in Statistics and Econometrics . Chichester.

    Google Scholar 

  • Mardia, Kantilal Vardichand/Goodall, Colin R. (1993): Spatio-temporal analysis of multivariate environmental data. In: G.P.Patil und C. R. Rao (Hrsg.), Multivariate Environmental Statistics, S.347-386. Amsterdam.

    Google Scholar 

  • Mardia, Kantilal Vardichand/Goodall, Colin R. /Redfern, Edwin J./Alonso, Francisco J. (1998): The kriged Kalman filter. Test 7(2), S.217-285.

    Article  Google Scholar 

  • Martin, Russell L./Oeppen, J.E. (1975): The identification of regional forecasting models using space-time correlation functions. Transactions of the Institute of British Geographers 66, S.95-118.

    Article  Google Scholar 

  • Meiring, Wendy/Guttorp, Peter/Sampson, Paul D..(1998): Space-time estimation of grid-cell hourly ozone levels for assessment of a deterministic model. Environmental and Ecological Statistics 5, S.197-222.

    Article  Google Scholar 

  • Miller, Robert N./Busalacchi, Antonio J./Hackert, Eric C. (1997): Applications of data assimilation to analysis of the ocean on large scales. Journal of the Meteorological Society of Japan 75, S.445-462.

    Google Scholar 

  • Pfeifer, Phillip E./Deutsch, Stuart Jay (1980a): Identification and interpretation of first order spacetime ARMA models. Technometrics 22, S.397-408.

    Article  Google Scholar 

  • Pfeifer, Phillip E./Deutsch, Stuart Jay (1980b): A three-stage iterative procedure for space-time modelling. Technometrics 22,S.35-47.

    Article  Google Scholar 

  • Phelan , Michael J./Goodall, Colin R. (1990): An assessment of a generalized WGR model for GATE rainfall. Journal of Geophysical Research – Atmospheres 95, S. 7603-7615.

    Article  Google Scholar 

  • Rouhani, Shahrokh/Myers, Donald E. (1990): Problems in space-time kriging of geohydrological data. Mathematical Geology 22 (5), S.611-623.

    Article  Google Scholar 

  • Rouhani, Shahrokh/Wackernagel,Hans (1990): Multivariate geostatistical approach to space-time data analysis. Water Resources Research 26 (4), S.585-591.

    Article  Google Scholar 

  • Sampson, Paul D./Guttorp, Peter (1992): Nonparametric estimation of nonstationary spatial covariance structure. Journal of the American Statistical Association.87, S.109-119.

    Article  Google Scholar 

  • Schach, Ulrike (2002): Vector Autoregressive Time Series Models with Spatial Dependence. Dissertation Universität Dortmund.

    Google Scholar 

  • Schlittgen, Rainer/Streitberg, Bernd H.J. (1997): Zeitreihenanalyse, 7. Auflage. München.

    Google Scholar 

  • Thiebaux , H. Jean (1997) : The power of the duality in spatial-temporal estimation. Journal of Climate 10, S. 567-573.

    Article  Google Scholar 

  • Waller,Lance A./Carlin, Bradley P./Xia, Hong/Gelfand, Alan E. (1997): Hierarchical spatiotemporal mapping of disease rates. Journal of the American Statistical Association 92, S. 607-617.

    Article  Google Scholar 

  • Wikle, Christopher K./Berliner, L.Mark/Cressie, Noel A.C. (1998): Hierarchical Bayesian spacetime models. Environmental and Ecological Statistics S.117-154.

    Google Scholar 

  • Wikle, Christopher K./Cressie, Noel A.C. (1999): A dimension-reduced approach to space-time Kalman filtering. Biometrika 86, S.815-830.

    Article  Google Scholar 

  • Wikle, Christopher K. (2000): Hierarchical space-time dynamic models. In: L.M. Berliner, D. Nychka und T.Hoar (Hrsg.), Studies in the Atmospheric Sciences – Lecture Notes in Statistics 144, S.45-64. New York.

    Google Scholar 

  • Wikle, Christopher K./Milliff, Ralph F./Berliner, L. Mark (2001): Spatio-temporal hierarchical Bayesian modeling – Tropical ocean surface winds. Journal of the American Statistical Association 96, S.382-397.

    Article  Google Scholar 

  • Xia, Hong/Carlin, Bradley B. /Waller, Lance A. (1997): Hierarchical models for mapping Ohio lung cancer rates. Environmetrics 8, S.107-120.

    Article  Google Scholar 

Download references

Authors
  1. Joachim Werner Otto Gerß
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Wolfgang Gerß

Rights and permissions

Reprints and permissions

Copyright information

© 2010 VS Verlag für Sozialwissenschaften | GWV Fachverlage GmbH

About this chapter

Cite this chapter

Gerß, J.W.O. (2010). Stochastische Modelle für Raum-Zeit-Daten. In: Gerß, W. (eds) Bevölkerungsentwicklung in Zeit und Raum. VS Verlag für Sozialwissenschaften. https://doi.org/10.1007/978-3-531-92113-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-531-92113-6_6

  • Publisher Name: VS Verlag für Sozialwissenschaften

  • Print ISBN: 978-3-531-17115-9

  • Online ISBN: 978-3-531-92113-6

  • eBook Packages: Humanities, Social Science (German Language)

Publish with us

Policies and ethics

Search

Navigation