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I am collecting air pollutant data for every area in a region. The available data I can find only has the data from stations in a few areas. Is it possible to estimate the air pollutant density for the rest of areas based on this data (e.g. density mapping)?

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  • $\begingroup$ I would guess, probably not. Monitoring stations may have been purposely located in places where pollution is worse than usual. Thus information from them may be helpful to assess efforts to clean up the air in known trouble spots, but hot helpful to assess region-wide air pollution. // In density mapping, monitoring stations will likely seem to be sources of pollution. 'Showing' pollution in areas not near a station will rest on assumptions that are difficult to verify. $\endgroup$ – BruceET Nov 2 '18 at 21:44
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There's lots of options out there for doing two-dimensional interpolation or regression. One attractive approach in this case would be to use a Gaussian Process model because: a) You may have independent evidence of the typical "smoothness" of the pollution over areas, which could be encoded precisely in a GP model, and b) It will give you information about your uncertainty due to lack of data in regions without the monitoring station.

BruceET's comment is very important here. You'll need to keep in mind any form of sampling bias introduced by the choice of placement of the monitoring stations.

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