Resilience Science » models

Systems theorist Vladimir Arnold has died

Garry Peterson — Sat, 12 Jun 2010 12:39:25 +0000

Vladimir I. Arnold one of the major creators of dynamical systems theory used to represent ecological regime shifts died June 3rd this year.

He was one of the creators of the mathematics behind what is known as catastrophe theory and singularity theory which are used to represent regime shifts. The New York Times writes:

Singularity theory predicts that under certain circumstances slow, smooth changes in a system can lead to an abrupt major change, in the way that the slipping of a few small rocks can set off an avalanche. The theory has applications in physics, chemistry and biology.

“He was a genius and one of the greatest and most influential mathematicians of our time,” said Boris A. Khesin, a former student of Dr. Arnold’s and now a professor of mathematics at the University of Toronto.

One of Dr. Arnold’s biggest contributions was applying the methods of geometry and symmetry to the motion of particles. Dr. Arnold work on how fluids flow was applied to the dynamics of weather, providing a mathematical explanation for why it is not possible to make forecasts months in advance. Infinitesimal gaps or errors in information cause forecasts to diverge completely from reality.

A similar approach can also be applied to the motion of planets. If Earth were the only planet to circle the Sun, its orbit would follow a precise elliptical path, but the gravity of the other planets disturbs the motion. Scientists found that it impossible to calculate the precise motion of the planets over very long periods of time or even prove that Earth will not one day be flung out of the solar system.

Understanding the subtle and difficult-to-predict boundary between stability and instability is important not only in the study of planetary dynamics but also in other endeavors, like designing a nuclear fusion reactor.

In 1954, the Russian mathematician Andrey Kolmogorov figured out a key insight to calculating whether such systems are stable. Dr. Arnold provided a rigorous proof in 1963 for one set of circumstances. Another mathematician, Jürgen Moser, provided the proof for another. The work is now collectively know at the KAM theory.

Andrew Gelman’s statistical lexicon

Garry Peterson — Sat, 20 Mar 2010 15:30:16 +0000

On his group’s weblog, influential Bayesian statistican Andrew Gelman proposes a statistical lexicon to make important methods and concepts related to statistics better know:

The Secret Weapon: Fitting a statistical model repeatedly on several different datasets and then displaying all these estimates together.

The Superplot: Line plot of estimates in an interaction, with circles showing group sizes and a line showing the regression of the aggregate averages.

The Folk Theorem: When you have computational problems, often there’s a problem with your model. …

Alabama First: Howard Wainer’s term for the common error of plotting in alphabetical order rather than based on some more informative variable.

The Taxonomy of Confusion: What to do when you’re stuck.

The Blessing of Dimensionality: It’s good to have more data, even if you label this additional information as “dimensions” rather than “data points.”

Scaffolding: Understanding your model by comparing it to related models.

Multiple Comparisons: Generally not an issue if you’re doing things right but can be a big problem if you sloppily model hierarchical structures non-hierarchically.Taking a model too seriously: Really just another way of not taking it seriously at all.

Computer trading producing new financial dynamics?

Garry Peterson — Fri, 29 Jan 2010 19:32:07 +0000

In October 1987, stock markets around the world crashed, with the Dow Jones droping 22%. The causes of this crash are still unclear, but one of the suspected causes was computer automated trading. This concern lead attempts to design mechanisms to break potential viscous cycles by creating ‘circuit breakers‘, rules that halt trading if the Dow rapidly . However, as financial engineers innovate, new risks are emerging. The Financial Times writes Computer-driven trading raises meltdown fears:

An explosion in trading propelled by computers is raising fears that trading platforms could be knocked out by rogue trades triggered by systems running out of control.

Trading in equities and derivatives is being driven increasingly by mathematical algorithms used in computer programs. They allow trading to take place automatically in response to market data and news, deciding when and how much to trade similar to the autopilot function in aircraft.

Analysts estimate that up to 60 per cent of trading in equity markets is driven in this way.

… Frederic Ponzo, managing partner at GreySpark Partners, a consultancy, said: “It is absolutely possible to bring an exchange to breaking point by having an ‘algo’ entering into a loop so that by sending them at such a rate the exchange can’t cope.”

Regulators say it is unclear who is monitoring traders to ensure they do not take undue risks with their algorithms.

The Securities and Exchange Commission has proposed new rules that would require brokers to establish procedures to prevent erroneous orders.

Mark van Vugt, global head of sales at RTS Realtime Systems, a trading technology company, said: “If a position is blowing up so fast without the exchange or clearing firm able to react or reverse positions, the firm itself could be in danger as well.”

For more details on current problems see the Financial Times article Credit Suisse fined over algo failures

NYSE Euronext revealed on Wednesday it had for the first time fined a trading firm for failing to control its trading algorithms in a case that highlights the pitfalls of the rapid-fire electronic trading that has come to dominate many markets.

The group, which operates the New York Stock Exchange, said it had fined Credit Suisse $150,000 after a case in 2007 when hundreds of thousands of “erroneous messages” bombarded the exchange’s trading system.

The messages, generated by the Credit Suisse proprietary trading algorithm, caused the trading system to slow down, affecting 900 share issues, according to Ray Pellechia, a NYSE Euronext spokesman.

Asked if the exchange’s systems could have been knocked out, he said: “If you had multiplied this many times you’d have had a problem on your hands.”

Shared pre-analytical vision, and groupthink and economics

Garry Peterson — Tue, 13 Jan 2009 22:36:15 +0000

On the Economix Blog, economist Uwe Reinhardt writes An Economist’s Mea Culpa that argues that economists have become locked into a too narrow pre-analytical vison of how the world works:

Fewer than a dozen prominent economists saw this economic train wreck coming — and the Federal Reserve chairman, Ben Bernanke, an economist famous for his academic research on the Great Depression, was notably not among them. Alas, for the real world, the few who did warn us about the train wreck got no more respect from the rest of their colleagues or from decision-makers in business and government than prophets usually do.

How could the economics profession have slept so soundly right into the middle of the economic mayhem all around us? Robert J. Shiller of Yale University, one of the sage prophets, addressed that question an earlier commentary in this paper. Professor Shiller finds an explanation in groupthink, a term popularized by the social psychologist Irving L. Janis. In his book “Groupthink” (1972), the latter had theorized that most people, even professionals whose careers ostensibly thrive on originality, hesitate to deviate too much from the conventional wisdom, lest they be marginalized or even ostracized.

If groupthink is the cause, it most likely is anchored in what my former Yale economics professor Richard Nelson (now at Columbia University) has called a ”vested interest in an analytic structure,” the prism through which economists behold the world.

This analytic structure, formally called “neoclassical economics,” depends crucially on certain unquestioned axioms and basic assumptions about the behavior of markets and the human decisions that drive them. After years of arduous study to master the paradigm, these axioms and assumptions simply become part of a professional credo. Indeed, a good part of the scholarly work of modern economists reminds one of the medieval scholastics who followed St. Anselm’s dictum “credo ut intellegam”: “I believe, in order that I may understand.”

Financial crisis: bad models or bad modellers

Garry Peterson — Wed, 12 Nov 2008 08:51:35 +0000

Australian economist, John Quiggin writes on Crooked Timber about the contribution of models to the financial crisis:

The idea that bad mathematical models used to evaluate investments are at least partially to blame for the financial crisis has plenty of appeal, and perhaps some validity, but it doesn’t justify a lot of the anti-intellectual responses we are seeing. That includes this NY Times headline In Modeling Risk, the Human Factor Was Left Out. What becomes clear from the story is that a model that left human factors out would have worked quite well. The elements of the required model are

in the long run, house prices move in line with employment, incomes and migration patterns

if prices move more than 20 per cent out of line with long run value they will in due course fall at least 20 per cent

when this happens, large classes of financial assets will go into default either directly or because they are derived from assets that can’t pay out if house prices fall

It was not the disregard of human factors but the attempt to second-guess human behavioral responses to a period of rising prices, so as to reproduce the behavior of housing markets in the bubble period, that led many to disaster. A more naive version of the same error is to assume that particular observed behavior (say, not defaulting on home loans) will be sustained even when the conditions that made that behavior sensible no longer apply.

…More generally, in most cases, the headline result from a large and complex model can usually be reproduced with a much simpler model embodying the same key assumptions. If those assumptions are right (wrong) the model results will be the same. The extra detail usually serves to produce more detailed results rather than to produce significant changes in the headline results.