Environmental and Ecological Statistics

, Volume 12, Issue 2, pp 225–243 | Cite as

Efficient statistical mapping of avian count data

Article

Abstract

We develop a spatial modeling framework for count data that is efficient to implement in high-dimensional prediction problems. We consider spectral parameterizations for the spatially varying mean of a Poisson model. The spectral parameterization of the spatial process is very computationally efficient, enabling effective estimation and prediction in large problems using Markov chain Monte Carlo techniques. We apply this model to creating avian relative abundance maps from North American Breeding Bird Survey (BBS) data. Variation in the ability of observers to count birds is modeled as spatially independent noise, resulting in over-dispersion relative to the Poisson assumption. This approach represents an improvement over existing approaches used for spatial modeling of BBS data which are either inefficient for continental scale modeling and prediction or fail to accommodate important distributional features of count data thus leading to inaccurate accounting of prediction uncertainty.

Keywords

breeding bird survey mapping count data poisson model random effects spatial prediction spatial modeling spatial statistics 

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References

  1. Berger, J.O., De Oliveira, V., Sansó, B. 2001Objective Bayesian analysis of spatially correlated dataJournal of the American Statistical Association96136174CrossRefGoogle Scholar
  2. Berliner, L.M., Lu, Z.-Q., Snyder, C. 1999Statistical design for adaptive weather observationsJournal of the Atmospheric Sciences56253652CrossRefGoogle Scholar
  3. Best, N.G., Waller, A., Thomas, A., Conlon, E.M., and Arnold, R.A. (1998) Bayesian models for spatially correlated disease and exposure data. in Bayesian Statistics 6, J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith (eds.), Oxford University Press, pp. 1–18.Google Scholar
  4. Bueso, J.M., Angulo, J.M., Alonso, F.J. 1998A state-space model approach to optimum spatial sampling design based on entropyEnvironmental and Ecological Statistics52944CrossRefGoogle Scholar
  5. Clayton, D.G. 1996

    Generalized linear mixed models

    Gilks, W.R.Richardson, S.Spiegelhalter, D.J. eds. Markov Chain Monte Carlo in PracticeChapman & HallLondon275301
    Google Scholar
  6. Cox, D.D, Cox, L.H., Ensor, K.B. 1996Spatial sampling for the environmentEnvironmental and Ecological Statistics421933CrossRefGoogle Scholar
  7. Cressie, N.A.C. 1991Statistics for Spatial DataJohn Wiley & SonsNew YorkGoogle Scholar
  8. Dietrich, C.R., Newsam, G.N. 1993A fast and exact method for multidimensional Gaussian stochastic simulationsWater Resources Research29286169CrossRefGoogle Scholar
  9. Diggle, P.J., Tawn, J.A., Moyeed, R.A. 1998Model-based geostatistics (with discussion)Applied Statistics47299350Google Scholar
  10. Flather, C.H., Sauer, J.R. 1996Using landscape ecology to test hypotheses about large-scale abundance patterns in migratory birdsEcology772835Google Scholar
  11. Fuentes, M. 2001A high frequency kriging approachEnvironmetrics1246983CrossRefGoogle Scholar
  12. Gelman, A., Rubin, D.B. 1992Inference from iterative simulation using multiple sequencesStatistical Science7457511Google Scholar
  13. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B. 1995Bayesian Data AnalysisChapman & HallLondonGoogle Scholar
  14. Gilks, W.R., Richardson, S., Spiegelhalter, D.J. 1995Markov Chain Monte Carlo in PracticeChapman & HallLondonGoogle Scholar
  15. Haas, T.C. 1992Redesigning continental-scale monitoring networksAtmospheric Environment26332333Google Scholar
  16. He, Z., Sun, D. 2000Hierarchical Bayes estimation of hunting success rates with spatial correlationsBiometrics4619299Google Scholar
  17. Higdon, D. 1998A process-convolution approach to modeling temperatures in the North Atlantic OceanJournal of Environmental and Ecological Statistics517390CrossRefGoogle Scholar
  18. Link, W.A., Sauer, J.R. 1997Estimation of population trajectories from count dataBiometrics536372Google Scholar
  19. Link, W.A., Sauer, J.R. 1997New Approaches to the Analysis of Population Trends in Land Birds: A comment on statistical methodsEcology78263234Google Scholar
  20. Mejia, J.M., Rodriguez-Iturbe, I. 1974On the synthesis of random field sampling from the spectrum: An application to the generation of hydrological spatial processesWater Resources Research1070511Google Scholar
  21. Nychka, D., Wikle, C.K., and Royle, J.A. (2002) Multiresolution Models for Nonstationary Spatial Covariance Functions. Statistical Modelling: In International Journal, 2, 315–331.Google Scholar
  22. Nychka, D. and Saltzman, N. (1998) Design of air-quality monitoring networks, in Case Studies in Environmental Statistics, D. Nychka, W. Piegorsch, and L. Cox (eds.), New York in ‘‘Lecture Notes and Statistics’’, vol. 132, Springer, 196 pp.Google Scholar
  23. Obled, C., Creutin, J.D. 1986Some developments in the use of empirical orthogonal functions for mapping meteorological fieldsJournal of Climate and Applied Meteorology251189204CrossRefGoogle Scholar
  24. Oehlert, G.W. 1996Shrinking a wet deposition networkAtmospheric Environment30134757CrossRefGoogle Scholar
  25. Robbins, C.S., Bystrak, D.A., and Geissler, P.H. (1986) The Breeding Bird Survey: its first fifteen years, 1965–1979. USDOI, Fish and Wildlife Service Resource Publication 157. Washington, D.C.Google Scholar
  26. Royle J.A., Link W.A., and Sauer J.R. (2001) Statistical mapping of count survey data. in Predicting Species Occurrences Issues of Scale and Accuracy, Scott, J.M., Heglund, P.J., Morrison, M., Raphael, M., Haufler, J. and Wall, B. (eds.), Island Press, Covello CA.Google Scholar
  27. Sauer, J.R., Peterjohn, B.G., Link, W.A. 1994Observer differences in the North American Breeding Bird SurveyAuk1115062Google Scholar
  28. Sauer, J.R., Pendleton, G.W., and Orsillo, S. (1995) Mapping of bird distributions from point count surveys. in monitoring bird populations by point counts C.J. Ralph, J.R. Sauer and S. Droege, (eds.), USDA Forest Service, Pacific Southwest Research Station, General Technical Report PSW-GTR-149, pp. 151–60.Google Scholar
  29. Shinozuka, M., Jan, C.M. 1972Digital simulation of random processes and its applicationsJournal of Sound Vibration2511128CrossRefGoogle Scholar
  30. Shumway, R.H. 1988Applied Statistical Time Series AnalysisPrentice-HallNew JerseyGoogle Scholar
  31. Shumway, R.H., Stoffer, D.S. 2000Time Series Analysis and Its ApplicationsSpringer-VerlagNew YorkGoogle Scholar
  32. Stein, M. 1999Interpolation of Spatial Data: Some Theory for KrigingSpringer-VerlagNew YorkGoogle Scholar
  33. Villard, M.A., Maurer, B.A. 1996Geostatistics as a tool for examining hypothesized declines in migratory songbirdsEcology775968Google Scholar
  34. Wikle, C.K., Cressie, N. 1999A dimension reduction approach to space-time Kalman filteringBiometrika8681529CrossRefGoogle Scholar
  35. Wikle, C.K., Milliff, R.F., Nychka, D., Berliner, L.M. 2001Spatiotemporal hierarchical Bayesian modeling: Tropical ocean surface windsJournal of the American Statistical Association9638297CrossRefMathSciNetGoogle Scholar
  36. Wikle, C.K. Royle, J.A. (2005) Dynamic design of ecological monitoring networks for non-Gaussian spatio-temporal data. Environmetrics (in press).Google Scholar
  37. Yang, K., Carr, D.B., and O’Connor, R.J. (1995) Smoothing of Breeding Bird Survey data to produce national biodiversity estimates. Computing Science and Statistics: Proceeding of the 27th Symposium on the Interface, pp. 405–09.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Division of Migratory Bird ManagementU.S. Fish and Wildlife ServiceLaurelUSA
  2. 2.Department of StatisticsUniversity of MissouriColumbiaUSA
  3. 3.USGS Patuxent Wildlife Research CenterLaurelUSA

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