Ok, I am required to tackle a very though problem with very limited knowledge of even basic statistics.
Basically I need to study the following:
1) I have a quantity randomly distributed over a 2D surface
2) I can take a limited number of samples, and I cannot freely choose the sampling locations due to physical constraints.
3) I have to infer the mean value assumed by the quantity over the surface with a given confidence.
4) I must take into consideration a strong spatial correlation of samples.
5) I believe that I also must take into consideration the spatial coverage of the sample (i.e. if I have three samples spaced 3ft apart taken from a 1000 sq ft surface (spatial domain), their representativity of the surface is very low, but if the surface is just 20 sq ft they are more likely to describe the surface properties)
How can I address this problem?