Bayesian hierarchical models for analysing the spatial distribution of bioclimatic indices

  1. Xavier Barber 1
  2. David Conesa 2
  3. Antonio López-Quílez 2
  4. Asunción Mayoral 1
  5. Javier Morales 1
  6. Antoni Barber
  1. 1 Centro de Investigación Operativa. Universidad Miguel Hernández de Elche
  2. 2 Dpt. Estadística i Investigació Operativa. Universitat de València
Revista:
Sort: Statistics and Operations Research Transactions

ISSN: 1696-2281

Año de publicación: 2017

Volumen: 41

Número: 2

Páginas: 277-296

Tipo: Artículo

DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Sort: Statistics and Operations Research Transactions

Resumen

A methodological approach for modelling the spatial distribution of bioclimatic indices is proposed in this paper. The value of the bioclimatic index is modelled with a hierarchical Bayesian model that incorporates both structured and unstructured random effects. Selection of prior distributions is also discussed in order to better incorporate any possible prior knowledge about the parameters that could refer to the particular characteristics of bioclimatic indices. MCMC methods and distributed programming are used to obtain an approximation of the posterior distribution of the parameters and also the posterior predictive distribution of the indices. One main outcome of the proposal is the spatial bioclimatic probability distribution of each bioclimatic index, which allows researchers to obtain the probability of each location belonging to different bioclimates. The methodology is evaluated on two indices in the Island of Cyprus.

€ Ver financiación

Información de financiación

Xavier Barber, David Conesa and Antonio López-Quílez would like to thank the Minis-terio de Economía y Competitividad (the Spanish Ministry of Economy and Finance) for its support in the form of the research grant MTM2016-77501-P (oj intly fi nanced with the European Regional Development Fund –FEDER–).

Financiadores

Referencias bibliográficas

  • Adams, N., Kirby, S., Harris, P. and Clegg, D. (1996). A review of parallel processing for statistical computation. Statistics and Computing, 6, 37–49.
  • Atkinson, P. and Tate, N. (2000). Spatial scale problems and geostatistical solutions: a review. The Professional Geographer, 52, 607–623.
  • Baltensperger A. and Huettmann, F. (2015). Predicted shifts in small mammal distributions and biodiversity in the altered future environment of alaska: an open access data and machine learning perspective. PloS one, 10, e0132054.
  • Banerjee, S., Carlin, B. and Gelfand, A. (2014). Hierarchical Modeling and Analysis for Spatial Data, Second Edition. Chapman and Hall/CRC, Boca Raton.
  • Bates, D. and Maechler, M. (2015). Matrix: Sparse and Dense Matrix Classes and Methods. R package version 1.2-0.
  • Blackford, L., Choi, J., Cleary, A., D’Azevedo, E., E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D. and Whaley, R. (1997). ScaLAPACK Users’ Guide. SIAM, Society for Industrial and Applied Mathematics, Philadelphia.
  • Britton, A., Pakeman, R., Carey, P., and Marrs, R. (2001). Impacts of climate, management and nitrogen deposition on the dynamics of lowland heathland. Journal of Vegetation Science, 12, 797–806.
  • Burrough, P. (2001). GIS and geostatistics: essential partners for spatial analysis. Environmental and Ecological Statistics, 8, 361–377.
  • Chambers, R. and Dunstan, R. (1986). Estimating distribution functions from survey data. Biometrika, 73, 597–604.
  • Cheddadi, R., Guiot, J. and Jolly, D. (2001). The Mediterranean vegetation: what if the atmospheric CO2 increased? Landscape Ecology, 16, 667–675.
  • Cuenca, J., Giménez, D. and González, J. (2004). Architecture of an automatically tuned linear algebra library. Parallel Computing, 30, 187–210.
  • De Oliveira, V. (2007). Objective Bayesian analysis of spatial data with measurement error. The Canadian Journal of Statistics, 35, 1–19.
  • Dongen, V. (2006). Prior specification in Bayesian statistics: three cautionary tales. Journal of Theoretical Biology, 242, 90–100.
  • Dostálek, J., Frantı́k, T. and Šilarová, V. (2014). Changes in the distribution of alien plants along roadsides in relation to adjacent land use over the course of 40 years. Plant Biosystems, (published online: 20 Dec 2014): 1–17.
  • Eddelbuettel, D., François, R., Allaire, J., Chambers, J., Bates, D. and Ushey, K. (2011). Rcpp: Seamless R and C++ integration. Journal of Statistical Software, 40, 1–18.
  • Finley, A., Banerjee, S. and Gelfand, A. (2015). spBayes for Large Univariate and Multivariate PointReferenced Spatio-Temporal Data Models. Journal of Statistical Software, 63, 1–28.
  • Gamerman, D. and Lopes, H. (2006). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. CRC Press, Boca Raton.
  • Garzón-Machado, V., Otto, R. and del Arco Aguilar, M.J. (2014). Bioclimatic and vegetation mapping of a topographically complex oceanic island applying different interpolation techniques. International Journal of Biometeorology, 58, 887–899.
  • Gelman, A., Carlin, J., Stern, H., Dunson, D., Vehtari, A. and Rubin, D. B. (2013). Bayesian Data Analysis, Third Edition. Chapman and Hall-CRC, Boca Raton.
  • Gilks, W., Richardson, S. and Spiegelhalter, D. (1996). Markov Chain Monte Carlo in Practice. Chapman and Hall, London.
  • Golub, G. and Van Loan, C. (1996). Matrix Computations, Third Edition. Johns Hopkins University Press, Baltimore.
  • Handcock, M. and Wallis, J. (1994). An approach to statistical spatial-temporal modeling of meteorological fields. Journal of the American Statistical Association, 89, 368–390.
  • Lee, P. (1997). Bayesian Statistics: an Introduction, Second Edition. Arnold, London.
  • Legendre, P., Borcard, D. and Peres-Neto, P. (2005). Analyzing beta diversity: partitioning the spatial variation of community composition data. Ecological Monographs, 75, 435–450.
  • Lunn, D., Thomas, A., Best, N. and Spiegelhalter, D. (2000). WinBUGS – A Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing, 10, 325–337.
  • Matérn, B. (1986). Spatial Variation, Second Edition. Springer-Verlag, Berlin.
  • Osborne, C., Mitchell, P., Sheehy, J. and Woodward, F. (2000). Modelling the recent historical mpacts of atmospheric CO2 and climate change on Mediterranean vegetation. Global Change Biology, 6, 445– 458.
  • Rivas-Martı́nez, S. (1994). Clasificación bioclimática de la tierra (bioclimatic classification system of the earth). Folia Botanica Matritensis, 13, 1–25.
  • Rivas-Martı́nez, S. and Rivas-Saenz, S. (2016). Worldwide Bioclimatic Classification System. Phytosociological Research Center. Spain, http://www.globalbioclimatics.org.
  • Rivas-Martı́nez, S., Rivas-Sáenz, S., Penas, A. et al. (2002). Worldwide Bioclimatic Classification System. Backhuys Pub.
  • Robertson, G. (1987). Geostatistics in ecology: interpolating with known variance. Ecology, 68, 744–748.
  • Rosenthal, J. (2000). Parallel computing and Monte Carlo algorithms. Far East Journal of Theoretical Statistics, 4, 207–236.
  • Rossi, R., Mulla, D., Journel, A. and Franz, E. (1992). Geostatistical tools for modeling and interpreting ecological spatial dependence. Ecological Monographs, 62, 277–314.
  • Rossini, A.J., Tierney, L. and Li, N. (2007). Simple parallel statistical computing in R. Journal of Computational and Graphical Statistics, 16, 399–20.
  • Sanderson, C. (2010). Armadillo: An open source C++ linear algebra library for fast prototyping and computationally intensive experiments. NICTA.
  • Stein, M. (1999). Interpolation of Spatial Statistics Data: Some Theory for Kriging. Springer-Verlag, New York.
  • Strupczewski, W., Kochanek, K., Weglarczyk, S. and Singh, V. (2007). On robustness of large quantile estimates to largest elements of the observation series. Hydrological Processes, 21, 1328–1344.
  • Tasser, E. and Tappeiner, U. (2002). Impact of land use changes on mountain vegetation. Applied Vegetation Science, 5, 173–84.
  • Whiley, M. and Wilson, S. (2004). Parallel algorithms for Markov chain Monte Carlo methods in latent spatial gaussian models. Statistics and Computing, 14, 171–179.
  • Yan, J., Cowles, M., Wang, S. and Armstrong, M. (2007). Parallelizing MCMC for Bayesian spatiotemporal geostatistical models. Statistics and Computing, 17, 323–335.
Fuente de los datos: Dialnet