Tom
> Would it be wise to state that if you only want the mean and variance =
> use block kriging, if you want a pdf = use conditional simulation?
Oh, yes, please do.
There are two ways to apply "discretisation".
One is to estimate each of the fine grid of points and store the weights for each sample. You can then aggregate (average) the estimates and compute the estimation variance for the overall average. This has been suggested by Cressie and can also serve for non-Normal distributions and their back-transforms. Takes a lot of computer time, but not nearly as much as simulation. Has the advantage of only using the short part of the semi-variogram model and the disadvantage of having to compute the estimation variance.
The other way is to directly krige the block average - one kriging system, one estimate with its
associated kriging variance. Has the advantage of being very fast, with the disadvantages of potentially large sparse matrices and using all of your semi-variogram model. The sparse matrix problems have been well discussed by such experts as Don Myers in Math Geol.
It is a common fallacy to trust the short distance semi-variogram and assume that model fit decreases with distance. In most cases, the bulk of pairs included in a semi-variogram graph are in the middle to larger distances - unless you go past the generally accepted distance of one-half maximum of study area. Models are actually most reliable in the middle. If you doubt this, try watching the (in)sensitivity of the Cressie goodness of fit measure when you change the nugget effect - and, hence, the initial slope of your model.
Isobel
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