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Estimating Distance Sampling Detection Functions When Distances Are Measured With Errors

  • David Borchers
  • Tiago Marques
  • Thorvaldur Gunnlaugsson
  • Peter Jupp
Article

Abstract

Distance sampling methods assume that distances are known but in practice there are often errors in measuring them. These can have substantial impact on the bias and precision of distance sampling estimators. In this paper we develop methods that accommodate both systematic and stochastic measurement errors. We use the methods to estimate detection probability in two surveys with substantial measurement error. The first is a shipboard line transect survey in the North Sea in which information on measurement error comes from photographically measured distances to a subset of detections. The second is an aerial cue-counting survey off Iceland in which information on measurement error comes from pairs of independently estimated distances to a subset of detections. Different methods are required for measurement error estimation in the two cases. We investigate by simulation the properties of the new estimators and compare them to conventional estimators. They are found to perform better than conventional estimators in the presence of measurement error, more so in the case of cue-counting and point transect estimators than line transect estimators. An appendix on the asymptotic distributions of conditional and full likelihood estimators is available online.

Key Words

Cue-counting Line transect Maximum likelihood Point transect 

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Supplementary material

13253_2010_21_MOESM1_ESM.pdf (156 kb)
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References

  1. Akaike, H. (1973), “Information theory and an extension of the maximum likelihood principle,” in Proceedings of 2nd International Symposium on Information Theory, eds. B. Petrov and F. Csáki, Budapest: Akadémiai Kiadó, pp. 267–281. Google Scholar
  2. Alpizar-Jara, R. (1997), “Assessing assumption violation in line transect sampling,” Ph.D. thesis, North Carolina State University, Raleigh. Google Scholar
  3. Borchers, D. L., Pike, D., Gunnlaugsson, T., and Vikingsson, G. A. (2009), “Minke whale abundance estimation from the NASS 1987 and 2001 cue-counting surveys taking account of distance estimation errors,” North Atlantic Marine Mammal Commission Special Issue. Google Scholar
  4. Buckland, S. T., and Anganuzzi, A. (1988), “Comparison of smearing methods in the analysis of minke sightings data from IWC/IDCR Antarctic cruises,” Report of the International Whaling Commission, 38, 257–263. Google Scholar
  5. Buckland, S. T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L., and Thomas, L. J. (2001), Introduction to Distance Sampling, Oxford: Oxford University Press. zbMATHGoogle Scholar
  6. Butterworth, D. S. (1982), “On the functional form used for g(y) for minke whale sightings, and bias in its estimation due to measurement inaccuracies,” Report of the International Whaling Commission, 32, 833–838. Google Scholar
  7. Chen, S. X. (1998), “Measurement errors in line transect surveys,” Biometrics, 54, 899–908. zbMATHCrossRefMathSciNetGoogle Scholar
  8. Chen, S. X., and Cowling, A. (2001), “Measurement errors in line transect sampling where detectability varies with distance and size,” Biometrics, 57, 732–742. CrossRefMathSciNetGoogle Scholar
  9. Fuller, W. (2006), Measurement Error Models (2nd ed.), New Jersey: Wiley. zbMATHGoogle Scholar
  10. Hiby, L., Ward, A., and Lovell, P. (1989), “Analysis of the North Atlantic sightings survey 1987: Aerial survey results,” Report of the International Whaling Commission, 39, 447–455. Google Scholar
  11. Leaper, R., Burt, M. L., Gillespie, D., and MacLeod, K. (unpublished), “Comparisons of measured and estimated distances and angles from sightings surveys,” IWC Document SC/60/IA6. Google Scholar
  12. Louis, T. A., and Zeger, S. L. (2009), “Effective communication of standard errors and confidence intervals,” Biostatistics, 10, 1–2. CrossRefGoogle Scholar
  13. Marques, T. A. (2004), “Predicting and correcting bias caused by measurement error in line transect sampling using multiplicative error models,” Biometrics, 60, 757–763. CrossRefMathSciNetGoogle Scholar
  14. Marques, F. F. C., and Buckland, S. T. (2003), “Incorporating covariates into standard line transect analyses,” Biometrics, 59, 924–935. zbMATHCrossRefMathSciNetGoogle Scholar
  15. Marques, F. F. C., and Buckland, S. T. (2004), “Covariate models for detection function,” in Advanced Distance Sampling, eds. S. T. Buckland, D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers and L. J. Thomas, Oxford: Oxford University Press. Google Scholar
  16. Thomas, L. J. T., Laake, J. L., Strindberg, S., Marques, F. F. C., Buckland, S. T., Borchers, D. L., Anderson, D. R., Burnham, K. P., Hedley, S. L., Pollard, J. H., Bishop, J. R. B., and Marques, T. A. (2008), Distance 5.0. Release 2, Research Unit for Wildlife Population Assessment, University of St Andrews, http://www.ruwpa.st-and.ac.uk/distance/.
  17. Williams, R., Leaper, R., Zerbini, A. N., and Hammond, P. S. (2007), “Methods for investigating measurement error in cetacean line transect surveys,” Journal of the Marine Biological Association of the UK, 87, 313–320. CrossRefGoogle Scholar

Copyright information

© International Biometric Society 2010

Authors and Affiliations

  • David Borchers
    • 1
  • Tiago Marques
    • 2
    • 3
  • Thorvaldur Gunnlaugsson
    • 4
  • Peter Jupp
    • 5
  1. 1.Centre for Research into Ecological and Environmental Modelling, The ObservatoryUniversity of St AndrewsFifeUK
  2. 2.Centre for Research into Ecological and Environmental ModellingUniversity of St AndrewsFifeUK
  3. 3.Centro de Estatística e Aplicações da Universidade de LisboaLisboaPortugal
  4. 4.Marine Research InstituteReykjavikIceland
  5. 5.School of Mathematics and Statistics, Mathematical InstituteUniversity of St AndrewsFifeUK

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