I am not sure if what I am trying to do is possible.. I have about 30 to 40 randomly distributed points in an area and I am trying to create a uniform kernel density surface that covers the points (i.e. the kernel density distribution will be constant for all points and taper off to zero around the edges - like a table top). I am sure I can adjust each point's weight (lower the weighting for points closer together and raise the weighting for points further apart) on an iterative basis to develop a uniform density surface but that will be time consuming and probably not be that accurate. Does anyone know if this is a) possible and b) if there is a package (in R or QGIS or ARCGIS etc.) available that automates a process like this? Please let me know if I have not been clear in my explanation as it all makes perfect sense to me in my mind.
I would try to use a weighted gridding process to create a uniform set of points. You would have to introduce a set of zero value control points so that the taper point is in the right place. I would use ZMAP, Geocap or Surfer
PS If you have the data and it is not confidential then I could give it a go. I would need the AOI and node spacing that you require
Try to use a median polish!
http://onlinelibrary.wiley.com/doi/10.1002/env.495/abstract
You may wish to pick up the thread in the literature for DEMP, Density Equalizing Map Projections. These can be thought of as "rubber sheeting" a surface so that the density of points on the surface is then of uniform density. You may also wish to read a bit about Cartograms, of which DEMP is a special case. It also is worth noting that most currently used spatial analysis methods can adjust for the underlying density of the thing being measured using heterogeneous Poisson models.
ArcGIS can easily create kriging surfaces from points using the interpolation tools.
With R, use "kde2d" to do a 2D kernel density estimation, which is part of the MASS package. For a really excellent visual, see "demo(rgl)" from the rgl package, and you will see the example near the end.
I would *not* recommend doing a spatial interpretation in QGIS/ArcGIS, as you will have difficulty constraining the shape to fulfil the properties of a pdf.
You could use Percent Volume Contour for creating a flat surface in vector format. Use Hawth Tool for ArcGis: http://www.spatialecology.com/htools/tooldesc.php
Craig, if I understand your question correctly, it sounds like what you are trying to do is assign a constant value across the area that each data point "represents". This could be done using Thiessen polygons or a distance allocation in ArcGis. Essentially assigning the value of each data point to the (collective) area closest to the data point. Worded differently, every point in the area assigned to a data point will be closer to that data point than any other point in your set of data points. If you wanted to think of it as a kernal function it would just be y = a constant. If you want a function between data points, that would be a TIN. I think someone else posted that option previously.
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