Transitive geostatistics and statistics per individual : a relevant framework for assessing resources with diffuse limits

Nicolas Bez

Journal de la société française de statistique (2007)

  • Volume: 148, Issue: 1, page 53-75
  • ISSN: 1962-5197

Abstract

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When assessing marine resources, inferring spatial models has to be performed from a unique realisation. The situations with repetitive surveys that can be considered as repetition of the same regionalized variable are (obviously) rare. In intrinsic geostatistics, this question is usually solved by a couple of key assumptions namely stationarity and ergodicity. Unfortunately, these assumptions and their consequences are often too strong with regards to the reality of fish survey data. It is especially unrealistic to assume that the spatial structure is independent from the geometry of field. Transitive geostatistics has proven to be an operational alternative to intrinsic geostatistics and was the seed for the development of a framework called “statistics per individual”. This article presents the rationale of the approach and sketches the main tools developed during the past few years with practical illustrations. Statistics per individual have the advantage to be simple and thus more robust than intrinsic approaches (robust in the sense that the properties of the estimator are based on fewer and checkable assumptions). On the one hand, “statistics per individual” allow for summarizing and describing series of spatial distributions into few quantitative features. On the other hand, as developed in the first ages of geostatistics, they allow for estimating global abundance with estimation variance thanks to the (transitive) covariogram and for interpolating between observations (transitive kriging). The price to pay for the simplicity of the method is that it leads to fewer possible applications than the intrinsic geostatistical approaches and that, as a design based approach, it is constrained to some specific sampling schemes (e.g. the regular, stratified regular or point process survey strategies).

How to cite

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Bez, Nicolas. "Transitive geostatistics and statistics per individual : a relevant framework for assessing resources with diffuse limits." Journal de la société française de statistique 148.1 (2007): 53-75. <http://eudml.org/doc/93456>.

@article{Bez2007,
abstract = {When assessing marine resources, inferring spatial models has to be performed from a unique realisation. The situations with repetitive surveys that can be considered as repetition of the same regionalized variable are (obviously) rare. In intrinsic geostatistics, this question is usually solved by a couple of key assumptions namely stationarity and ergodicity. Unfortunately, these assumptions and their consequences are often too strong with regards to the reality of fish survey data. It is especially unrealistic to assume that the spatial structure is independent from the geometry of field. Transitive geostatistics has proven to be an operational alternative to intrinsic geostatistics and was the seed for the development of a framework called “statistics per individual”. This article presents the rationale of the approach and sketches the main tools developed during the past few years with practical illustrations. Statistics per individual have the advantage to be simple and thus more robust than intrinsic approaches (robust in the sense that the properties of the estimator are based on fewer and checkable assumptions). On the one hand, “statistics per individual” allow for summarizing and describing series of spatial distributions into few quantitative features. On the other hand, as developed in the first ages of geostatistics, they allow for estimating global abundance with estimation variance thanks to the (transitive) covariogram and for interpolating between observations (transitive kriging). The price to pay for the simplicity of the method is that it leads to fewer possible applications than the intrinsic geostatistical approaches and that, as a design based approach, it is constrained to some specific sampling schemes (e.g. the regular, stratified regular or point process survey strategies).},
author = {Bez, Nicolas},
journal = {Journal de la société française de statistique},
keywords = {single realisation; transitive geostatistics; covariogram; design-based estimation variance},
language = {eng},
number = {1},
pages = {53-75},
publisher = {Société française de statistique},
title = {Transitive geostatistics and statistics per individual : a relevant framework for assessing resources with diffuse limits},
url = {http://eudml.org/doc/93456},
volume = {148},
year = {2007},
}

TY - JOUR
AU - Bez, Nicolas
TI - Transitive geostatistics and statistics per individual : a relevant framework for assessing resources with diffuse limits
JO - Journal de la société française de statistique
PY - 2007
PB - Société française de statistique
VL - 148
IS - 1
SP - 53
EP - 75
AB - When assessing marine resources, inferring spatial models has to be performed from a unique realisation. The situations with repetitive surveys that can be considered as repetition of the same regionalized variable are (obviously) rare. In intrinsic geostatistics, this question is usually solved by a couple of key assumptions namely stationarity and ergodicity. Unfortunately, these assumptions and their consequences are often too strong with regards to the reality of fish survey data. It is especially unrealistic to assume that the spatial structure is independent from the geometry of field. Transitive geostatistics has proven to be an operational alternative to intrinsic geostatistics and was the seed for the development of a framework called “statistics per individual”. This article presents the rationale of the approach and sketches the main tools developed during the past few years with practical illustrations. Statistics per individual have the advantage to be simple and thus more robust than intrinsic approaches (robust in the sense that the properties of the estimator are based on fewer and checkable assumptions). On the one hand, “statistics per individual” allow for summarizing and describing series of spatial distributions into few quantitative features. On the other hand, as developed in the first ages of geostatistics, they allow for estimating global abundance with estimation variance thanks to the (transitive) covariogram and for interpolating between observations (transitive kriging). The price to pay for the simplicity of the method is that it leads to fewer possible applications than the intrinsic geostatistical approaches and that, as a design based approach, it is constrained to some specific sampling schemes (e.g. the regular, stratified regular or point process survey strategies).
LA - eng
KW - single realisation; transitive geostatistics; covariogram; design-based estimation variance
UR - http://eudml.org/doc/93456
ER -

References

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  1. [1] Bez N., J. Rivoirard and Ph. Guiblin (1997). Covariogram and related tools for structural analysis of fish survey data. Kluwer Academic Publisher, E.Y. Baafi and N.A. Schofield (eds), Geostatistics Wollongong’96, Volume 2, 1316-1327. MR1602647
  2. [2] Bez N. (2002). Global fish abundance estimation from regular sampling: the geostatistical transitive method. Canadian Journal of Fisheries and Aquatic Sciences, 59: 1921-1931. 
  3. [3] Bez N., and Rivoirard J. (2000a). Indices of collocation between populations. In : Checkley, D.M., J.R. Hunter, L. Motos, and C.D. van der Lingen (eds). Report of a workshop on the use of Continuous Underway Fish Egg Sampler (CUFES) for mapping spawning habitat of pelagic fish. GLOBEC Report 14, 1-65 pp. 
  4. [4] Bez N., and Rivoirard J. (2000b). On the role of sea surface temperature on the spatial distribution of early stages of European mackerel (1989) using inertiograms. ICES Journal of Marine Science, 57: 383-392. 
  5. [5] Bez N. and Rivoirard J. (2001). Transitive geostatistics to characterize spatial aggregations with diffuse limits: an application on mackerel ichtyoplankton. Fish. Res. 50: 41-58. 
  6. [6] Bez N., Rivoirard J., and Poulard J.C. (1995). Approche transitive et densités de poissons. Compte-rendu des journées de Géostatistique, 15-16 juin 1995, Fontainebleau, France. Cahiers de Géostatistique 5 161-177. 
  7. [7] Chilès J.P., and Delfiner P. (1999). Geostatistics, modeling spatial uncertainty. John Wiley and Sons, New York. Zbl0922.62098MR1679557
  8. [8] Conan G.Y., Moriyasu M., Wade E., and Comeau M. (1988). Assessment and spatial distribution surveys of snow crab stocks by geostatsistics. ICES C.M. 1988/K :10. 
  9. [9] Cressie N.A.C. (1991). Statistics for spatial data. Wiley, New York. Zbl0799.62002MR1127423
  10. [10] Faraj A. and Bez N. (2007). Spatial pattern of the Octopus vulgaris life cycle in the Southern North Atlantic off Morocco. ICES Journal of Marine Science, in press. 
  11. [11] Hoag S., Williams G., Myhre R., and McGregor R. (1980). Halibut assessement data: setline surveys in the North Pacific ocean, 1963-1966 and 1976-1979. International pacific halibut commission, technical report n°18, 42 p. 
  12. [12] ICES (2003). Report of the working group on mackerel and horse mackerel egg surveys. International Council for the Exploration of the Sea, Lisbon 2003, ICES CM 2003/G:7, 60 p. 
  13. [13] ICES (1997). Report of the International Bottom Trawl Survey Working Group. ICES CM/1997H:6. 
  14. [14] Jakobsen T., Korsbrekke K., Mehl S., and Nakken O. (1997). Norwegian combined acoustic and bottom trawl surveys for demersal fish in the Barents Sea during winter. ICES CM Y:17, 25 pp. 
  15. [15] Matheron G. (1965). Les variables régionalisées et leur estimation. Masson et Cie, Paris. 
  16. [16] Matheron G. (1971). The theory of regionalized variables and its applications. Les Cahiers du Centre de Morphologie Mathématique 5. 
  17. [17] Matheron G. (1989). Estimating and chosing: an essay on probability in practice. Springer, Berlin. Zbl0665.60002MR979761

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