Syzygy

Wednesday, May 13, 2009

Fisheries, Finance, and Physics

[edited for clarity]

See what I did there with the phonetic alliteration? :)

Q. What is the difference between the LHC (Large Hadron Collider) and Banks?

A. Black holes created by the LHC are more transparent about where stuff goes...



One theory about the potential dangers associated with the LHC puts the risk of it destroying the Earth at 50-50 (watch the clip!). Of course, this must be qualified by examining the probability that this theory of assessing the risk of the LHC is correct (0%). Other estimates of the risk posed by the LHC suggest that the probability of destroying the Earth is at 10^-9. As Ord, HIllerbrand, & Sandberg rightly point out, this should be qualified by the possibility that the model is incorrect or that calculation errors have been made.

In most cases, it is impossible to gauge the failure probability for something like a single bolt on the space shuttle. In these cases, mathematical models are often used. Clearly, estimates of the probability of "rare" events need to take into account the possibilities that the models used to generate such probabilities are accurate.

Andy Haldane describes a similar problem with how the financial industry assessed risk: some of the initial events that sparked the issue were "unlikely"* Well, either we are extremely "lucky" or the model is incorrect. Unless you can demonstrate to me that the probability of the latter is less likely than seeing that kind of impossible event, I'm going to bet that someone somewhere screwed up. In fact, it's plain to see from Chart 1 of the notes for Haldane's speech how this could happen. In the chart, data collected over the last 10 years (1998-2007) suggested that the probability of negative GDP growth was, effectively, zero. Looking over the whole sample of time (1857-2007) in which this data has been collected, however, suggests that negative GDP growth occurs maybe 15% of the time. That doesn't seem like a big difference, but when you bet billions of dollars on what you think is a sure thing (non-negative GDP growth), but actually occurs maybe 1 in 7 times, that's an f-ing big risk.

What does this have to do with Fisheries, you ask. Well, according to the Magnuson-Stevens Act (yep, THAT Ted Stevens), "Conservation and management measures shall be based upon the best scientific information available.". I suppose this means that fishing should not be a level where there is a significant risk of collapse. (whatever significant means...) Of course, the estimation of collapse risk is done using a model, which is fallible, possibly with high probability. If your best available science is not very good, is that sufficient to go plowing (or trawling, I guess) ahead? Your "best" model may suggest that you can fish 100,000 tons per year with < 1% chance of collapse, but if your model is only ~80% accurate (which is really good for fisheries models!), the upper bound on the probability of actual collapse is closer to 21% (0.8 * 1% + 0.2 * x, where x is unknown, but up to 1, potentially).

Logic and stats are nice when they're applied correctly, but more often than not, their use is exaggerated. And part of the blame does rest on the shoulder of scientists, who necessarily play up their results to get funding/acclaim/jobs. Still, that *is* why we have scientists advising the government, right? So that government officials will be able to take the best information available to make decisions? (and then we cross our fingers that our elected officials (or their appointees) know enough to weigh information properly...)

* shifts on the order of 25 standard deviations, which Andy calculates to occur roughly once every 10^135 years or
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 years.

1) Ord, T., Hillerbrand, R., & A. Sandberg. Probing the improbable: methodological challenges for risks with low probabilities and high stakes. [preprint] (2009).

2) Haldane, A.G. Why banks failed the stress test. [speech] (http://www.bankofengland.co.uk/publications/speeches/2009/speech374.pdf) (2009).

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