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

Journal de la société française de statistique (2007)

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

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topBez, 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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- [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] 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.
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- [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] ICES (1997). Report of the International Bottom Trawl Survey Working Group. ICES CM/1997H:6.
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- [15] Matheron G. (1965). Les variables régionalisées et leur estimation. Masson et Cie, Paris.
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