Hi people, Finally I got the point of argues for the estimation of population variance.
What I had in mind as an "overall" variance is the variance of all possible locations in any realization of the random field, while Isobel and some other people are trying to explain to me is the variance of all possible realization at any location of the random field. I realized, by noticing this, why along the discussion the stationarity and existence of variance has been emphasized. If the random field is not stationary then we'll have no consistant population variance as Isobel explained. I also learned that my understanding of the population variance has a name called "areal variance." Now, it should be clear why I emphasized on the expected variance of the "future samples." This would be the variance of the any possible sample taken from the current realization (which I called "population" previously) by some planned sampling scheme. And this variance will have to do with the clustering or non-clustering of the future sampling scheme. I'm aware, of course, that in practice "future" samples may no longer be taken from the current realization since in the real case the study site would be changing. Calling it a "future" sample is just a convenient saying for the expected variance based on possible sampling schemes. Hope I'm not getting things more confused. Mng-yng
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