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I find the combination of Bayes, diffuse priors, and the Kalman Filter to be very appealing & a useful linear model.
Neat stuff.
The basic idea behind the Kalman filter, IMO at least, is to have a good model for the uncertainty in the data. In other application areas, this uncertainty can be related to noise or other fluctuations which is then used to for example extract a signal from noise. In the model presented here the uncertainty about the mean is really meant to represent fluctuations in the volume sampled, or also in terms of what we think the volume that we sampled. So in this regard we can try to extract the growth in discoveries from the underlying dispersion.
The latter uncertainty is also very critical as input to extraction models, because our estimation of, e.g., how much reserve we have, is crucial input to the amount of effort we expend on getting the stuff out.
Can you use a substitute model for comparison? Such as the number of dry holes per successful hole, with a slope adjusted for increasing data confidence due to better imaging and drill guidance?
"Dig your heels firm unto dirt; and where is the dirt going..?" -Frank Herbert, "The Jesus Incident"
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To add to your KF description, I learned the KF (long ago) via recasting the standard OLS problem in the KF framework. I liked being able to 'see' the impact on the parameter estimates as data points were added to the time series: I found the explicit signal-noise decomposition the KF provides to be 'illuminating'.