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I have been interested in the following method, since I read about it in "Ship of Gold in the Deep Blue Sea"
http://en.wikipedia.org/wiki/Bayesian_statistics
I am working to flatten the Lower 48 HL plot, by looking for small overlooked oil fields. While small, the fields can be quite valuable. For example, with the right reservoir, a 500 acre area could produce 5 mb of oil. If Simmons is right about oil prices, this 500 acre area could generate a gross cash flow to the working interest owners and royalty owners of a billion dollars, in constant 2005 dollars. Which of course is fine, until the rioters appear at the gates of the mansions of the energy producers.
Private security is one of the most rapidly growing industries in the U.S. Globally, I wonder how many private security men are employed in the oil industry? My suspicion is that the number is quite large and growing in double digits each year. This factor is getting to be a significant cost of doing business.
Bayes rocks.
I know a decent amount of it, but not enough to express competence. I've done a couple of conference papers using Bayesian models, but that's because a buddy is much harder core Bayes than myself.
The frequentist world is a lot easier (central limit theorem, yadda, yadda), but Bayes makes a lot more intuitive sense. The math, however, is a lot harder.
I recommend Jeff Gill's Bayes book, if you're interested:
http://www.amazon.com/Bayesian-Methods-Behavioral-Sciences-Approach/dp/1...
(the estimation of priors, on the other hand, by this crowd, would be pretty good. *laugh*)
I'll probably get the book.
If you haven't read about the SS Central America, here is the link: http://www.amazon.com/Ship-Gold-Deep-Blue-Sea/dp/0349110999/ref=pd_bbs_s...
It's a remarkable story, from the sinking of the ship, and the rescue of some of the passengers, to the search for the wreck.
Prof. Goose,
IMO, the best introduction to Bayesian statistics is still the classic by Leonard J. Savage, "Foundations of Statistics." After sixty years, that text has stood the test of time. I remember struggling with the book back when I was fifteen years old and smarter than I am now, but after a few rereadings and working of problems I finally got it. (I may not be exceptionally bright, but I am exceptionally persistant.)
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"
Web -
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'.