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93 comments on A Nice Counterexample

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Stuart Staniford on October 1, 2005 - 3:10pm Permalink | Subthread | Parent | Comments top
But empirically that works very badly for the US, Romania, Norway, etc. So it doesn't seem interesting to push that model further.
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WebHubbleTelescope on October 1, 2005 - 7:13pm Permalink | Subthread | Parent | Comments top
I agree with the other commenters, you have to slow way down on this analysis.  I think you are violating Occam's razor by attributing something complicated and not physically possible (i.e. the logistic model) to something that can be explained away much more simply.

The more I look at it, the more I dislike plotting aP/CP against CP. I once was told a story long ago by my father who described going to a talk by another engineer who was very excited about this great correlation he found in his data set.   The data points were very well aligned, all falling along a straight line. Well, as it turned out, the engineer had plotted X against X!  

And that is part of the problem. We ought to not contaminate one already dependent variable onto the axis of the other variable -- unless you are relatively sure that this fits some realistic behavior (c.f. the "drunk looking for his keys under the streetlight" scenario).  And I think the non-linear behavior we consistently see rules out the logistic model.

I have a post up describing the quasi-hyperbolic behavior that likely fits better here:
http://mobjectivist.blogspot.com/2005/09/oil-shock-model.html
and a more recent post showing how the math also describes the behavior of a simple electical RC circuit here:
http://mobjectivist.blogspot.com/2005/09/rc-circuit-analogy.html

But I also have to agree that the extra bump provided by new discoveries in North Sea oil tends to once again flatten out the slope. After all, every earlier discovery accomplished the same thing!

And don't take this criticism wrong. If you tried publishing this in any scientific journal as I and many others are accustomed to, you will have to be prepared to go through the ringer in your analysis. It's just that referees are much less common on the internet than in academic circles, as it doesn't come with the job description and it won't help anybody get tenure.

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Stuart Staniford on October 1, 2005 - 7:30pm Permalink | Subthread | Parent | Comments top
There's nothing physically impossible about the logistic model. It's obviously a simplification, but any model of an entire civilization is going to be a simplification. My perspective in such a situation is the more parameters we throw at it, the worse our predictions will be. You obviously differ, as you have a perfect right to do. I find your approach less persuasive than Hubbert's. I suggest you try it on partial histories for Romania or the US and see if you would have predicted the rest of the data better than the Hubbert linearization. If you can, that would get me to sit up and pay attention.

I have significant experience getting modeling work published in scientific fora, some of which has been very influential - scholar.google me for details. But these posts are work in progress (as I think should be obvious). No doubt publication will eventually follow when I think I have the story figured out to my own satisfaction.

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WebHubbleTelescope on October 1, 2005 - 8:54pm Permalink | Subthread | Parent | Comments top
Er, ok.  Looking at how you have been using the logistic model in the past --as a variant of the "pedator-prey" class of processes-- I think your modeling premise will have greater viability when applied to another pressing issue of today, that of the potential spread of avian flu. That is, if it firmly takes hold as some of the epidemiologists predict.

So is that really how Hubbert, Deffeyes, and others set up the  original peak oil math? By using a "predator-prey" model? Oh my, no wonder that people like Michael Lynch and company are having a field day in dissembling these kinds of models. It's common practice in those circles to simply trash another's model (i.e. policy); Lynch then doesn't even have to come up with his own.  Look at how well this strategy works in today's political circles.

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Stuart Staniford on October 1, 2005 - 9:37pm Permalink | Subthread | Parent | Comments top
Yes, the logistic equation is used in epidemiology - they call it the SI model (S=susceptible, I=infected). Essentially it is a model which is potentially applicable to any situation in which some initially exponentially growing process uses up some finite resource - whether it's a biological disease infecting a vulnerable population of animals, a computer worm using up a vulnerable population of computers, a new product spreading through a potential market, a new piece of information spreading through a financial market, or a civilization using up a finite pool of oil.

Fundamentally, it is an empirical question whether or not the model applies to oil production. No-one would claim it's going to be a perfect fit (or no-one with any sense, anyway!) but it has done a reasonably decent job in the very mature production areas (but not in the early stages). Stare at Romania again:

But there are certainly regions where it could mislead you without care (eg the UK). I'm engaged in trying to develop insight into where we might expect it to work, and where we might not.

As to Lynch et al. Critics serve a very valuable purpose in noting the holes and driving the improvements that need to be made. However, it's always much easier to criticise than make some constructive proposal oneself. No-one remembers the critics - they remember the people who make developments that actually improve the state of the art. Hubbert will be remembered far longer than Lynch, even though I respect Lynch as Hubbert's best critic: he has done some actual hard work and made critiques that serve a useful purpose.

And again - if you can develop a better model, more power to you. But the proof of that is showing that you can predict forward with smaller residuals for a broader class of situations.

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WebHubbleTelescope on October 1, 2005 - 11:26pm Permalink | Subthread | Parent | Comments top
For Romania, say they had a single oil strike some time in the past. Therefore, the forcing function looks like a delta function, and the solution set is just the exponential function if you assume production is proportional to the amount remaining (i.e. the stripper well scenario). Then when you plot dQ/dt/Q vs Q you get exp(-kt)/(1-exp(-kt)) plotted vs (1-exp(-kt)). In the regime where the logistic graph appears linear and it gets close to 90%, so does the exponential. And the match gets better if you put a bit of a spread in the delta function. Therefore you cannot tell the difference and the exponential model wins out because it matches a real physical process.

I don't respect Lynch at all. I agree with many people that think he is intellectually dishonest.

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Stuart Staniford on October 1, 2005 - 11:54pm Permalink | Subthread | Parent | Comments top
The logistic will start working before peak, the exponential decline will only start working after peak (eventually, they look identical, as you note).
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WebHubbleTelescope on October 2, 2005 - 1:00am Permalink | Subthread | Parent | Comments top
No, the logistic model does not work before the peak. It looks very susceptible to initial conditions. Looking right does not mean it is right.

The exponential model works over every regime. It just needs a  forcing function to create a spread in starting points.

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Dave Cohen on October 1, 2005 - 11:42pm Permalink | Subthread | Parent | Comments top
Re: "Yes, the logistic equation is used in epidemiology - they call it the SI model (S=susceptible, I=infected). Essentially it is a model which is potentially applicable to any situation in which some initially exponentially growing process uses up some finite resource..."

VERY interesting.... Write a post about this.

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Stuart Staniford on October 1, 2005 - 11:56pm Permalink | Subthread | Parent | Comments top
I thought I did.
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Dave Cohen on October 2, 2005 - 4:45am Permalink | Subthread | Parent | Comments top
No, you didn't. What I meant was the meaning of the linearization function in different domains (oil production, epidemiology, etc.), the intuitive generalization of the model in different domains. If this model has general applicability, then demonstrate it. Show that future oil production is modeled in the same way as the spread of the 1918 flu virus (in the worse case). What you have never expressed is the intuition behind the model. This is important.
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WebHubbleTelescope on October 2, 2005 - 1:32am Permalink | Subthread | Parent | Comments top
The problem is that there is nothing exponentially growing. There is a cumulatively growing set of tapped reserves, which takes work and time to find. This is offset by a depletion activity which is proportional to the amount of oil in each new reserve tapped. Unfortunately this does not describe the logistic model, which is more suited to the epidemiological and ecological sciences, and also to some fairly arcane chemical growth models that I did my thesis work on in the 80's.  Trust me, no way does this model work for oil depletion. It just happens to give an empirical fit. And people have started building heuristics around this model. Bad idea.

Now knowing what the basis of the logistic model was before today, I keep wanting to imagine little Pac-man oil molecules gobbling each other up.  I will probably have nightmares over this tonight.

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Stuart Staniford on October 2, 2005 - 12:51pm Permalink | Subthread | Parent | Comments top
There is something (very roughly) exponentially growing - the amount of information, capital, equipment, etc applied to the region - go read the Mineral Economy.. Whether you like it or not, you are modeling a social process interacting with a physical process - both in the finding of the oil, in how quickly people choose to develop it, and in what kind of technology they apply to the extraction process (horizontal wells at the top of the oil layer are not likely to lead to an exponential dropoff, for example). Again, you can complain all you like, but until you show me your lower residual fits to a broad range of situations, you don't have anything. I at least am weary of discussing it with you for now since we do not seem to making any progress. Come back with your superior fits to the data.
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WebHubbleTelescope on October 2, 2005 - 3:16pm Permalink | Subthread | Parent | Comments top
In the logistic equation, you use the term "a" and "1-a" to refer to a quantity and its complement. Now you want to use "a" to refer to some some economic scalar that grows exponentially, while "1-a" to refer to the oil reservoir itself. That makes absolutely no sense from a mathematical point of view, as in mixing apples and oranges.  Unless someone establishes a physical relationship between "a" and "1-a", I wouldn't go near solving this equation. And if there were a relationship, it might not be linear.  In that case, the tidyness of the solution evaporates.

In the normal predator-prey relationships, you can get away with this stuff because you are ony dealing with discrete entities that have at least an empirical relationship. For example, it takes N rabbits to sustain a single fox. Or one virus to infect one unprotected computer. Or an anion and a cation to generate a molecule. But where does this relationship come up here?  

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Stuart Staniford on October 2, 2005 - 12:56pm Permalink | Subthread | Parent | Comments top
I meant to say superior predictions - you can always get superior fits by overfitting - the test is can you predict forward from partial histories with lower residuals.
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