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Updated Verhulst model

Discuss research and forecasts regarding hydrocarbon depletion.
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Unread postby khebab » Tue 05 Jul 2005, 10:33:28

$this->bbcode_second_pass_quote('pup55', 'T')hanks, Khebab and Energyspin for improving the level of dialogue. I am just being Aristotilian.

http://peakoil.com/fortopic3218.html

You will enjoy the conversation of our Lotka-Volterra model as it applies to oil depletion.

Thanks pup55 for having initiated this thread! it shows that online exchange of ideas can be very instructive and exciting!

Thank you Energyspin for your long posts and your desire to share your impressive knowledge! It's gonna take me a few days to digest all your posts! :-D
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Unread postby EnergySpin » Tue 05 Jul 2005, 15:09:49

$this->bbcode_second_pass_quote('', 'T')hank you Energyspin for your long posts and your desire to share your impressive knowledge! It's gonna take me a few days to digest all your posts!

I have exams in less than 2 months... but I have to say that instead of wasting away the long weekend surfing for music, I did something productive. Now to turn the others from apocalyptic gloomers to plain doomers?
The problem I see, is that people see the equation of depletion and do not comprehend how they can affect it. ASPO did a great job to push for cooperation ... but the last newsletter ... it seems they might be pushing for a certain political agenda instead. Sites like dieoff.org and homing on Odulvai collapse do not help either - they fail to mention the assumptions that underlie their predictions and metrics. People see the math and think we are doomed, the invisible hand is reaching up to give me nasty rectal exam .... but fail to see how their collective actions are represented in the math.
Fatalism is going to be fatal; yes NA is going to be hit harder but this means a lot more focused work instead of whining, stashing weapons and all that stuff.
Cubans did it ... in 10 years they were back to 90% food production compared to their peak .. and their oil supply was cut overnight. In the process they lost 20lbs and had to rely on community owned TV and internet. I dont see how a 20lb wt loss could be harmful to the slobs we have here, and a loss of a 102 inch home theater is not the end of the world. So maybe we stand a better chance, unless people decide to go for an Orwellian state hoping that their McMansion extravaganza will be saved by killing off the 'tards'/blacks/Jews/3rdworlders/immigants/gay/lesbians/Christians/Muslims
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Unread postby WebHubbleTelescope » Sun 10 Jul 2005, 15:23:19

$this->bbcode_second_pass_quote('EnergySpin', '')$this->bbcode_second_pass_quote('', 'T')hank you Energyspin for your long posts and your desire to share your impressive knowledge! It's gonna take me a few days to digest all your posts!

I have exams in less than 2 months... but I have to say that instead of wasting away the long weekend surfing for music, I did something productive. Now to turn the others from apocalyptic gloomers to plain doomers?


Pat yourself on the back for knocking back the liquor while fitting to a bunch of closed-form expressions.

I am not going to go toe-to-toe with any of the attempts you made at trying to fit the coefficients of a set of closed-form expressions. However, I think the premise of using those expressions is misguided.

If you look at it from an engineering standpoint, we would try to separate out the temporal response from the temporal stimulus. Discoveries act as the forcing function and unless these get deconvolved from the production curves, we can't make any sense about the "named" functions you are referring to.

No closed form expression matches that allows one to understand what the [Verhulst,Logistics] curve coefficients mean physically.

Plug in whatever a priori discovery curves we have already and then do the convolution and maybe we get get a better fundamental and intuitive understanding of what's going on.
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Unread postby EnergySpin » Sun 10 Jul 2005, 15:37:32

$this->bbcode_second_pass_quote('', 'P')lug in whatever a priori discovery curves we have already and then do the convolution and maybe we get get a better fundamental and intuitive understanding of what's going on.

1)Oil is being depleted fast :)
2)These models make sense af averages ... i.e. once oil was gone and one had the completed data .... one could estimate the average depletion over the production history
3)Verhulst and logistic DO have an intuitive meaning ... like mean field approximations to more refined models
4) I do not claim any fame ... the answer probably requires refined modelling like the use of a multi step Verhulst or an SDE approach (I have already mentioned that)
5) Why are being rude?
"Nuclear power has long been to the Left what embryonic-stem-cell research is to the Right--irredeemably wrong and a signifier of moral weakness."Esquire Magazine,12/05
The genetic code is commaless and so are my posts.
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Unread postby WebHubbleTelescope » Sun 10 Jul 2005, 17:41:06

$this->bbcode_second_pass_quote('EnergySpin', '
')3)Verhulst and logistic DO have an intuitive meaning ... like mean field approximations to more refined models


Intuitive, yes. Like 2 eggs is more intuitive than 2.3735 eggs.

I can clean up on this wasteland of buzzwords.

Here is some straight talk on how to approach the modeling:
http://mobjectivist.blogspot.com/2005/0 ... model.html


I won't apologize for rudeness. Let the chips fall where they may to expose mathematical posturing. pedantic -> Oil depletion is one of the world's biggest problems and if you find things wrong with what somebody does, call their methods on it.

Anyways you were the one saying you were knocking back vodka and whatever.
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Unread postby EnergySpin » Sun 10 Jul 2005, 17:51:24

Misunderstandings at all levels (your part and my part)
The original thread was on Verhulst modeling , we did not discuss more advanced models till we hit the section of the "Discussion of Results" :)

My point is that all these exercises have mathematical pitfalls. I do not maintain I found the secret ... but I did report what I consider major problems with the way Nonlinear Regression is applied and why it might even be impossible to accurately fit data on the Verhulst.
And unless someone (ASPO/USGS/BP) provide people with prediction and quality-contro statistics that NLS estimation theory (irrespective of frequentist/Bayesian interpretation) demands ... then any over-optimistic or over-pessimistic projection should be disregarded.
But irrespective of these general comments, it is intriguing that in all of these exercises D-Day is sometime between 2006-2008
"Nuclear power has long been to the Left what embryonic-stem-cell research is to the Right--irredeemably wrong and a signifier of moral weakness."Esquire Magazine,12/05
The genetic code is commaless and so are my posts.
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Unread postby EnergySpin » Sun 10 Jul 2005, 18:00:29

For what is worth ... my experience with the Verhulst ...

I played around with simulated data sets generated using the Verhulst. As the algorithm approaches the solution, the curves generated by using the parameters at the bounds of the 99.99% intervals get narrower if you have data at least 3 years prior the peak (or better after the peak).
Due to the biased nature of the estimators, the estimated curve that comes closer to the theoretical one is the 99.99% curve (has to do with the bias of the estimated parameters)
Now ...running the simulations again using the original data that was posted in the Updated Verhulst heading up to 2008 and watching for the behaviour I mentioned (i.e. estimated curves in the 99.99% interval that are close together) I get the following:
Peak Oil date 2007.848
Peak Production: 39.221 (? is this realistic?)
Parameters : {2714, 1.16049, 16.5753, 108.884}
The second best (one iteration shorter run)
Peak Oil date : 2006.216
Parameters: {Qinf->2197.35, thl -> 103.617, n -> 0.585863, τ -> 16.5978}
Peak Production: 37.9982
Any of the numbers sound iffy? (esp peak production capacity)
"Nuclear power has long been to the Left what embryonic-stem-cell research is to the Right--irredeemably wrong and a signifier of moral weakness."Esquire Magazine,12/05
The genetic code is commaless and so are my posts.
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Unread postby EnergySpin » Sun 10 Jul 2005, 18:06:01

Another set of predictions ... using Lowess to smooth the production data series firs

My predictions (and I did estimate Qinf from data) are as follows (range is the 95% CI). I give the expected value for the peak (too lazy to start Monte Carlo/Bayesian integrations)
Peak sometime in 2005
Qinf = 2870 (2870.81, 2870.83)
t1/2 = 114.589 (113.999, 115.178)
n = 2.35 (2.12145, 2.57855)
τ = 18.6098 (17.9191,19.2997)

Letting Levenberg Screw around a little bit more
.... peak is 2006
Qinf = 3435.62 (3435.61, 3435.62)
t1/2 =125.316 (125.095, 125.538)
n = 3.46561 (3.38928,3.54195)
τ = 18.211 (17.9688,18.4532)

... peak is 2009
Qinf = 4562 (4562.65, 2562.66)
t1/2 = 147.562 (147.411,147.712)
n = 5.698 (5.58753,5.80942)
τ = 17.4548 (17.1761,17.7334)

The difference is caused by letting optimization ran from 21->22->23 iterations. I think scenario 1 is the correct one.
And WebbleHubTelescope, If you want to PM to send you the Mathematica notebook that was used to generate these data
"Nuclear power has long been to the Left what embryonic-stem-cell research is to the Right--irredeemably wrong and a signifier of moral weakness."Esquire Magazine,12/05
The genetic code is commaless and so are my posts.
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