Abstract
This paper develops a Bayesian approach for spatial inference on animal density from line transect survey data. We model the spatial distribution of animals within a geographical area of interest by an inhomogeneous Poisson process whose intensity function incorporates both covariate effects and spatial smoothing of residual variation. Independently thinning the animal locations according to their estimated detection probabilities results into another spatial Poisson process for the sightings (the observations). Prior distributions are elicited for all unknown model parameters. Due to the sparsity of data in the application we consider, eliciting sensible prior distributions is important in order to get meaningful estimation results. A reversible jump Markov Chain Monte Carlo (MCMC) algorithm for simulation of the posterior distribution is developed. We present results for simulated data and a real data set of minke whale pods from Antarctic waters. The main advantages of our method compared to design-based analyses are that it can use data arising from sources other than specifically designed surveys and its ability to link covariate effects to variation of animal density. The Bayesian paradigm provides a coherent framework for quantifying uncertainty in estimation results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aldrin, M., Holden, M., and Schweder, T. (2003), “Comment on ‘Spatial Methods for Line Transect Surveys,’ by A. Cowling,” Biometrics, 59, 186–188.
Buckland, S. T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L., and Thomas, L. (2001), Introduction to Distance Sampling, Oxford: Oxford University Press.
Buckland, S. T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L., and Thomas, L. (eds.) (2004), Advanced Distance Sampling, Oxford: Oxford University Press.
Cowling, A. (1998), “Spatial Methods for Line Transect Surveys,” Biometrics, 54, 828–839.
Diggle, P. J. (2003), Statistical Analysis of Spatial Point Patterns (2nd ed.), London: Arnold.
Ferreira, J. T. A. S., Denison, D. G. T., and Holmes, C. C. (2002), “Partition Modelling,” in Spatial Cluster Modelling, eds. A. B. Lawson and D. G. T. Denison, Boca Raton: Chapman and Hall/CRC, pp. 125–145.
Gilks, W. R., Richardson, S., and Spiegelhalter, D. J. (eds.) (1996), Markov Chain Monte Carlo in Practice, London: Chapman and Hall.
Green, P. J. (1995), “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination,” Biometrika, 82, 711–732.
Hagen, G. S., and Schweder, T. (1995), “Point Clustering of Minke Whales in the Northeastern Atlantic,” in Whales, Seals, Fish and Man, eds. A. S. Blix, L. Walløe, and Ø. Ulltang, Amsterdam: Elsevier, pp. 27–33.
Hedley, S. L., and Buckland, S. T. (2004), “Spatial Models for Line Transect Sampling,” Journal of Agricultural, Biological, and Environmental Statistics, 9, 181–199.
Heikkinen, J., and Arjas, E. (1998), “Non-Parametric Bayesian Estimation of a Spatial Poisson Intensity,” Scandinavian Journal of Statistics, 25, 435–450.
Ickstadt, K., and Wolpert, R. L. (1999), “Spatial Regression for Marked Point Processes” (with discussion), in Bayesian Statistics 6, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford: Oxford University Press, pp. 323–341.
Møller, J., Syversveen, A. R., and Waagepetersen, R. P. (1998), “Log Gaussian Cox Processes,” Scandinavian Journal of Statistics, 25, 451–482.
Skaug, H. J. (2006), “Markov Modulated Poisson Processes for Clustered Line Transect Data,” Environmental and Ecological Statistics, 13, 199–211.
Schweder, T. (1974), “Transformation of Point Processes: Application to Animal Sighting and Catch Problems, with Special Emphasis on Whales,” unpublished Ph.D. thesis, University of California, Berkeley.
— (1977), “Point Process Models for Line Transect Experiments,” in Recent Developments in Statistics, eds. J. R. Barra, B. Van Cutsem, F. Broadeau, and G. Romier, Amsterdam: North-Holland, pp. 221–242.
Snyder, J. P. (1987), Map Projections—A Working Manual, U.S. Geological Survey Professional Paper 1395, Washington, United States Government Printing Office. Available at http://pubs.er.usgs.gov/usgspubs/pp/pp1395.
Stoyan, D., Kendall, W. S., and Mecke, J. (1995), Stochastic Geometry and its Applications (2nd ed.), Chichester: Wiley.
Tanner, M. A., and Wong, W. H. (1987), “The Calculation of Posterior Distributions by Data Augmentation” (with discussion), Journal of the American Statistical Association, 82, 528–550.
van Dyk, D. A., and Park, T. (2008), “Partially Collapsed Gibbs Samplers: Theory and Methods,” Journal of the American Statistical Association, 103, 790–796.
Waagepetersen, R., and Schweder, T. (2006), “Likelihood-Based Inference for Clustered Line Transect Data,” Journal of Agricultural, Biological, and Environmental Statistics, 11, 264–279.
Williams, R., Hedley, S. L., and Hammond, P. S. (2006), “Modeling Distribution and Abundance of Antarctic Baleen Whales Using Ships of Opportunity,” Ecology and Society, 11 [online] URL: http://www.ecologyandsociety.org/vol11/iss1/art1/.
Wolpert, R. L., and Ickstadt, K. (1998), “Poisson/Gamma Random Field Models for Spatial Statistics,” Biometrika, 85, 251–267.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Niemi, A., Fernández, C. Bayesian Spatial Point Process Modeling of Line Transect Data. JABES 15, 327–345 (2010). https://doi.org/10.1007/s13253-010-0024-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13253-010-0024-8