Stochastic approaches work when you have a statistically useful set. If you average enough fields, you might come up with a model that you can apply to similar large sets. It is possible that the random "above ground factors" cancel out, and the remaining behavior is related to geology and normal production logistics. But this behavior hardly be useful for predicting a single field (or well).

Stochastic approaches are being used to come up with better estimates for porosity and permeability in heterogeneous reservoirs such as the Arab-D carbonate. Kringing (interpolating) between widely spaced wells and 3D seismic still leaves much to be desired. You still can't predict what an individual well will do, but it might help in deciding where to put it (i.e. place your bets). You can search around and find a few examples such as:

http://www.spe.org/elibrary/servlet/spepreview?id=SPE-104496-MS&speCommo...

Web -- I suppose I'm not one of those empiricist geologists. I've been pretty much a development/reservoir geologist my whole career. Virtually all my work has focused on stochastic analysis. I suppose this is the distinction between those of us who work production histories vs. those without hard data speculating of on the "what if" possibilities out there. If anything I tend to ignore what the "book" says about theoretical production models. But when you have hard data refuting those models it's easy to do.

And thus we are back to the primary problem with the KSA numbers. IMO even if we just had the change in water cut over time for each well we could make much more reliable estimate of future production levels then any theoretical reservoir model. Of course, there's much more data then water cut to be mined but at least it would give a glimpse into the current state of the system.