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Hierarchical modeling for extreme values observed over space and time

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Abstract

We propose a hierarchical modeling approach for explaining a collection of spatially referenced time series of extreme values. We assume that the observations follow generalized extreme value (GEV) distributions whose locations and scales are jointly spatially dependent where the dependence is captured using multivariate Markov random field models specified through coregionalization. In addition, there is temporal dependence in the locations. There are various ways to provide appropriate specifications; we consider four choices. The models can be fitted using a Markov Chain Monte Carlo (MCMC) algorithm to enable inference for parameters and to provide spatio–temporal predictions. We fit the models to a set of gridded interpolated precipitation data collected over a 50-year period for the Cape Floristic Region in South Africa, summarizing results for what appears to be the best choice of model.

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References

  • Banerjee S, Carlin BP, Gelfand AE (2004) Hierarchical modeling and analysis for spatial data. Chapman and Hall/CRC Press

  • Besag J (1974). Spatial interaction and the statistical analysis of lattice systems. J Roy Stat soc, Ser B, (Methodol) 36: 192–236

    Google Scholar 

  • Besag J, Green PJ, Higdon D and Mengersen K (1995). Bayesian computation and stochastic systems. Stat Sci 10(1): 3–66

    Article  Google Scholar 

  • Coles SG and Tawn JA (1996). Modeling extreme of the areal rainfall processes. J Roy Stat Soc, Ser B, (Methodol) 58: 329–347

    Google Scholar 

  • Coles SG (2001). An introduction to statistical modeling of extreme values. Springer-Verlag, New York

    Google Scholar 

  • Cooley D, Nychka D and Naveau P (2007). Bayesian spatial modeling of extreme precipitation return levels.. J Am Stat Assoc 102: 824–840

    Article  CAS  Google Scholar 

  • Dahan E and Mendelson H (2001). An extreme value model of concept testing. Manage Sci 47: 102–116

    Article  Google Scholar 

  • Durman CF, Gregory JM, Hassell DC, Jones RG and Murphy JM (2001). A comparison of extreme European daily precipitation simulated by a global and regional climate model for present and future climates. Q J Roy Meteorol Soc 127: 573

    Article  Google Scholar 

  • Gelfand AE and Smith AFM (1990). Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 85(410): 398–409

    Article  Google Scholar 

  • Gelfand AE and Vounatsou P (2002). Proper multivariate conditional autoregressive models for spatial data analysis. Biostatistics 4: 11–25

    Article  Google Scholar 

  • Gelfand AE, Schmidt AM, Banerjee S and Sirmans CF (2004). Nonstationary multivariate process modelling through spatially varying coregionalization (with discussion). Test 13(2): 1–50

    Article  Google Scholar 

  • Gelman A (2003) Bayesian data analysis. CRC Press

  • Heffernan JE and Tawn JA (2003). A conditional approach for multivariate extreme values. J Roy Stat Soc, Ser B, (Methodol) 66: 497–546

    Article  Google Scholar 

  • Hewitson BC and Crane RG (2005). Gridded area-averaged daily precipitation via conditional interpolation. J Climate 18: 41–57

    Article  Google Scholar 

  • Huerta G and Sansó B (2007). Time-varying models for extreme values. Environ Ecol Stat 14: 285–299

    Article  CAS  Google Scholar 

  • Jin X, Carlin BP and Banerjee S (2005). Generalized hierarchical multivariate CAR models for areal data. Biometrics 61: 950–961

    Article  PubMed  Google Scholar 

  • Kharin VV and Zwiers FW (2005). Estimating extremes in transient climate change simulations. J Climate 1: 1

    Article  Google Scholar 

  • Mardia KV (1988). Multi-dimensional multivariate Gaussian Markov random fields with application to image processing. J Multivariate Anal 24: 265–284

    Article  Google Scholar 

  • Roberts SJ (2000). Extreme value statistics for novelty detection in biomedical Signal Processing. IEE Proc Sci Technol Meas 47(6): 363–367

    Article  Google Scholar 

  • Spiegelhalter DJ, Best NG, Carlin BP and van der Linde A (2002). Bayesian measures of model complexity and fit (with discussion). J Roy Stat Soc, Ser B, (Stat Methodol) 64(4): 583–639

    Article  Google Scholar 

  • Thompson ML, Reynolds J, Cox LH, Guttorp P and Sampson PD (2001). A review of statistical methods for the meteorological adjustment of tropospheric ozone. Atmos Environ 35: 617–630

    Article  Google Scholar 

  • West M and Harrison J (1997). Bayesian forecasting and dynamic models. Springer Verlag, New York

    Google Scholar 

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Authors and Affiliations

  1. Institute of Statistics and Decision Sciences, Durham, NC, USA

    Huiyan Sang & Alan E. Gelfand

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  1. Huiyan Sang
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  2. Alan E. Gelfand
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Correspondence to Huiyan Sang.

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Sang, H., Gelfand, A.E. Hierarchical modeling for extreme values observed over space and time. Environ Ecol Stat 16, 407–426 (2009). https://doi.org/10.1007/s10651-007-0078-0

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  • DOI: https://doi.org/10.1007/s10651-007-0078-0

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