On uncertainty and predictions

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

Many 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.