Two forms of spatial interpolation, the interpolation of point and areal data, are distinguished Traditionally, point interpolation is applied to isarithmic, that is, contour mapping and areal int

Spatial Interpolation Methods: A Review

Person, place, time: these are the basic elements of outbreak investigations and epidemiology. Historically, however, the focus in epidemiologic research has been on person and time, with little regard for the implications of place or space even though disease mapping has been done for over a hundred years. The development of geographic information systems (GISs) over the last 20 years has provided a more powerful and rapid ability to examine spatial patterns and processes. This, in turn, has fostered the discussion of such policyrelevant issues as health services and planning (1), as well as the use of GISs for epidemiologic investigations and disease surveillance. Methods of spatial analysis are given little, if any, introduction in modern epidemiology texts, and few epidemiologists have ventured further than making dot or choropleth maps, or listing geographic units along with rates of disease in tabular form (2-6). Spatial patterns are frequently intricate and complex, while most spatial methods used by epidemiologists can capture or identify only gross, simplistic patterns (2). Epidemiologists understand that disease processes have an historical (time) component, and formal methods of time series and hazard analyses are well-developed to study them. Few, however, recognize that every epidemic also has a geography (space). Some epidemiologists may not be aware that evaluation of the spatial distribution of measures of disease risk may provide etiologic insight. The logic of using geography to study disease or health care is derived from appreciation of factors causing non-uniformity of disease distribution (2). These fac-

/pdf/spatial-analytical-methods-and-geographic-information-244pkz55b8.pdf

Spatial Analytical Methods and Geographic Information Systems: Use in Health Research and Epidemiology

4 Departement de Geomatique, Laboratoire SURFACES, Universite de Liege, 7 place du 20 Aout (A1), 4000 Liege, Belgium ABSTRACT: The distribution of foraging activity for female Antarctic fur seals was investigated at Cap Noir (49° 07' S, 70° 45' E), Kerguelen Island in February 1998. Eleven females were fitted with a satellite transmitter and time-depth recorder. The 2 data sets were combined in order to locate diving activity of the seals. The occurrence of fish in the diet of the seals was investigated by the identifica- tion of otoliths in 55 scats collected at the breeding colony during the study period. Oceanographic variables were measured simultaneously by direct sampling and satellite remote sensing. The mesopelagic fish community was sampled at 20 stations along 4 transects, where epipelagic trawls were conducted at night at 50 m depth. We then investigated, using geographic information systems, the relationship between the spatial distribution of diving activity of the seals and oceanographic variables (sea surface temperature, surface chlorophyll concentration, prey distribution and bathy- metry) at the same spatio-temporal scale. An inverse relationship was found between the main fish species preyed on by the fur seals and those sampled in trawl nets. However, diving activity of the seals was significantly related to oceanographic conditions, forage fish distribution and distance from the colony, although these relationships changed with the spatial scale investigated. A probabilistic model was developed for the distribution of diving activity, which predicted where females should concentrate their foraging activity according to the oceanographic conditions of the year, and where breeding colonies should be located.

/pdf/spatial-distribution-of-foraging-in-female-antarctic-fur-5956uuwzdx.pdf

Spatial distribution of foraging in female Antarctic fur seals Arctocephalus gazella in relation to oceanographic variables: a scale-dependent approach using geographic information systems

Modelling urban population density in a multi-centered city.

This study introduces a hybrid spatial modelling framework, which accounts for spatial non‐stationarity, spatial autocorrelation and environmental correlation. A set of geographic spatially autocorrelated Euclidean distance fields (EDF) was used to provide additional spatially relevant predictors to the environmental covariates commonly used for mapping. The approach was used in combination with machine‐learning methods, so we called the method Euclidean distance fields in machine‐learning (EDM). This method provides advantages over other prediction methods that integrate spatial dependence and state factor models, for example, regression kriging (RK) and geographically weighted regression (GWR). We used seven generic (EDFs) and several commonly used predictors with different regression algorithms in two digital soil mapping (DSM) case studies and compared the results to those achieved with ordinary kriging (OK), RK and GWR as well as the multiscale methods ConMap, ConStat and contextual spatial modelling (CSM). The algorithms tested in EDM were a linear model, bagged multivariate adaptive regression splines (MARS), radial basis function support vector machines (SVM), Cubist, random forest (RF) and a neural network (NN) ensemble. The study demonstrated that DSM with EDM provided results comparable to RK and to the contextual multiscale methods. Best results were obtained with Cubist, RF and bagged MARS. Because the tree‐based approaches produce discontinuous response surfaces, the resulting maps can show visible artefacts when only the EDFs are used as predictors (i.e. no additional environmental covariates). Artefacts were not obvious for SVM and NN and to a lesser extent bagged MARS. An advantage of EDM is that it accounts for spatial non‐stationarity and spatial autocorrelation when using a small set of additional predictors. The EDM is a new method that provides a practical alternative to more conventional spatial modelling and thus it enhances the DSM toolbox. HIGHLIGHTS: We present a hybrid mapping approach that accounts for spatial dependence and environmental correlation. The approach is based on a set of generic Euclidean distance fields (EDF). Our Euclidean distance fields in machine learning (EDM) can model non‐stationarity and spatial autocorrelation. The EDM approach eliminates the need for kriging of residuals and produces accurate digital soil maps.

Spatial modelling with Euclidean distance fields and machine learning

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An introduction to trend surface analysis

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An introduction to trend surface analysis