On uncertainty and predictions

7 January, 2014 at 13:20 | Posted in Statistics & Econometrics | 10 Comments

falling coconuts signMany things that occur in the business world may not be predictable, but their unpredictability can at least be modeled. In other words, there are two types of uncertainty that practitioners need to be aware of. We call them subway and coconut uncertainty, respectively, and we’ll explain by way of a story.

Let’s imagine a character called Pierre … One of his passions is recording how long it takes him to get to work each morning via Paris’s highly efficient Métro system …

The graph of Pierre’s daily commuting times fits the well-known bell-shaped curve of the normal distribution. In his statistics class, he learned that almost all the values in a normal distribution lie within three standard deviations of the mean, while 95% lie within two standard deviations. There are almost no extreme values; most of Pierre’s journey times are clustered neatly around the average of 43 minutes. The graph represents what we call “subway uncertainty.” It effectively models the time it takes Pierre to get to his office each morning, together with the uncertainty of being earlier or later than the average. Indeed, Pierre has used it to make probabilistic predictions of how long his journey will take — and was satisfied to find that his forecasts were accurate. Pierre’s model makes some important assumptions. To begin, it assumes that future days are drawn from the same distribution as was observed in the past. Provided there is no major change — a prolonged shutdown of the entire Métro system, interruptions to the city’s power supply, a strike — that is a safe assumption. As long as there’s continuity between the past and future, the model is reliable.

In addition to liking a reliable commute, Pierre also likes exotic vacations. Unfortunately, on a trip to Thailand he had a deadly accident. While seeking shade under a palm tree, a coconut fell on his head. Our unlikely hero was the victim of a highly unlikely event that we call “coconut uncertainty” — a kind of freak happening that you just can’t plan for. The truth is that most real-life situations are mixtures of subway and coconut uncertainty, which is precisely why coconut uncertainty interests us.

In technical terms, coconut uncertainty can’t be modeled statistically using, say, the normal distribution. That’s because there are more rare and unexpected events than, well, you’d expect. In addition, there’s no regularity in the occurrence of coconuts that can be modeled. And we’re not just talking about Taleb’s “black swans” — truly bizarre events that we couldn’t have imagined. There are also bubbles, recessions and financial crises, which may not occur often but do repeat at infrequent and irregular intervals …

Given the number of disastrously bad forecasts — and not just in the last few years — it’s clear that businesses need a different strategy to cope with coconut uncertainty … The key is not to develop precise plans based on predictions, but to have emergency plans for a variety of possibilities. If you live in Paris, it’s not necessary to plan for an earthquake or a piece of a satellite falling from the sky. But there are some actions you can take that can protect you from events you cannot predict. Indeed, many of us already do so by purchasing insurance or practicing fire drills in the workplace. Most insurance policies cover a wide range of potential disasters, and the evacuation techniques practiced for fire would be just as well suited for bomb scares, floods or gas leaks.

Spyros Makridakis et al.



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  1. I recently studied Nassim Nicholas Talebs manuscript “The Science of Hidden Risks”, where he proposes methods for improved modelling and introduces fragility. He proposes a method to decrease the impact of bad models, since the consequences of model errors can be modelled.

    “it is much better to start with a real problem, understand it well on its own terms, then go find a mathematical tool (if any, or use nothing as is often the best solution) than start with mathematical theorems then find some application to these.”

    I think it should have been stressed much more clearly that using nothing is the best solution.

    What is quantitative methodology in the social sciences? Whether good or bad statistical method, what is it that is actually done?

    Introducing quantitative methods in the social sciences is to introduce an ultraconservative approach to society, when you create a quantitative tool to influence decisions in the real world, you allow these decisions to be guided by historical data. Quantitative method is simply a desire to project the society as it is and once was into the future, the desire to create a consensus to preserve the social structures described by the mathematics. It is this that is the main argument against quantitative method, the quantitative method was created to describe static systems, it was developed in the natural sciences, where the constants change so slowly that they can be considered as constants, a static system that moves in a time scale so incredibly long that mathematical models become relevant. This is not true in many other areas, it becomes doubtful already in biology and in the social sciences it is insanity. The reactionary and conservative principle is built into the mathematics, it is not an outspoken ambition, but it exists in mathematics that is used. But the mathematics produced for natural science contains more disturbing things when applied in social science. It contains an extreme reductionism, so extreme that the whole universe finally is reduced to emmanate from a single point. In the social sciences, this becomes fascism, no one is pronounced fascist of those involved in the quantitative method, it’s just built into the tools they use. It forces a consensus through mathematics, which denies any conflict, any dialectic relationship in society. In economics, it becomes a totalitarian planned political economy, no matter what you have in mind with the quantitative method.

    Quantitative methods and modelling in the social sciences cannot be improved, it cannot be reformed for good, if we shall develop foreward as a society we must cease this activity. There is no other way foreward for the social sciences and human development.

    • I hope you wont mind if I say, as a mathematician, that I agree with 99% of what you say. The 1% is where you say, for example, that “Quantitative methods and modelling in the social sciences cannot be improved”. It seems to me that Turing’s mathematical model of morphogenesis is of great importance to biology and that the underlying mathematics can be applied to economics (and other social sciences) to show the folly of the classical reductionist approach. In brief, Turing’s ‘critical instabilities’ matter!

      So while I would agree that the kind of ‘mathematical methods’ typically used in economics should cease, I would propose that the replacement activity might involve more (proper) mathematics, as well as less of what Keynes called pseudo-mathematics. (Although I wouldn’t like to put a number on my ‘belief’ in this.)

      • I generalize a bit too far ofcourse. There is little harm in me as a small player doing some maths on social happenings, studying some detail mathematically has no harm, but when these things become institutionalized it has profound effects on society.

        I arrived at economics as a chemist annoyed with the thermodynamics analogy. Thanks for the suggestion to read about Turing.

    • Human beings are in the last and final stage of their evolution and their life form is obsolete and actually very dangerous for all other life forms. Soon human life will be preserved in a simulation. There is no future to a life form whose critical aspects are governed by a Pareto distribution. http://www.digitalcosmology.com/Blog/2012/12/11/the-new-digital-world/

      • Are you governed by a Pareto distribution? My condolences.

      • I am and you are if you are a true part of this planet. Unless in your parallel universe, 50% of richest people control only 20% of the wealth. But not in this universe. http://en.wikipedia.org/wiki/Pareto_principle#In_economics

        Power laws, including some physical ones like the law of gravity, make life on this planet very difficult and eventually problematic.

      • I would not read too much into Pareto distribution, I would have to define the society as it is to be Utopia, a finished society, beyond development. I view it as an emergence.

        Interesting text about automation. It is basically describing Marx Tendency of the rate of profit to fall, which ofcourse is accelerating in a globalized world and it is accelerated by quantitative methods. That principle threatens the Pareto distribution and may be the very thing that breaks it. When technology pushes the tendency of the rate of profit to fall, the respons will first be to use the state to force the customers to pay, as in media industry, to use the state to maintain Pareto distribution. As this principle is accelerated with a globalized computer network and quantitative methods, it will eventually eliminate profits, since profits are non-thermodynamic, requiring non-equilibrium and barriers/pseudobarriers to exist.

        Replacing money with digital money is merely a stop gap measure to maintain economy and currency as we know it. What is the real point of money, what is the most basic thing that money facilitates, that we tell school-children is the point of currency? To faciitate transaction. In a globalized world, where we have a global network of machines that can instantly connect production with need/want, what use do we have for economy, for currency?

  2. Nice analogies. He is the King of Forecasting.

    • As a frequent visitor to London who tends to talk to the locals while on holiday, I thought that falling coconuts were more reasonably thought of as being stochastic than are subway trains.

      Much UK transport has multi-modal delays. I agree on the need for a different strategy, though.

      • Both setups are stochastic in the sense that they are described by random variables and their distributions. The problem with the “coconuts” is that the distributions are unknown besides the fact that an event may be quite painful 🙂

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