A Signal in the Noise

Subsequent to the national acclaim achieved by Nate Silver for his accurate predictions of the 2012 senatorial and presidential elections, I was moved to read his recently published book, The Signal and the Noise, to see how a master of prediction looks at the world. Somewhat to my surprise, I found that the book contains no cut-and-dry algorithm for making good predictions. Instead, The Signal and the Noise primarily focuses on the opposite question: why is it so hard to make accurate predictions?

Silver frames his discussion of the art of prediction with an observation made by Philip Tetlock, a professor at the University of Pennsylvania. Tetlock, borrowing from an essay by Isaiah Berlin, classifies people into two categories: hedgehogs and foxes. Hedgehogs are people who know “one big thing.” They are people who tend to prefer using a single theory to explain everything, ignoring information and overlooking arguments that would call their approach into question. Foxes, on the other hand, are less self-confident about their abilities, constantly looking for new approaches and revising their methodology in light of new information. Foxes, according to Tetlock, are much better at making predictions than hedgehogs. The key to making accurate predictions is a willingness to look at a problem from all angles and to consider all relevant information, not to look for a “silver bullet” theory that will explain everything. Silver also cautions, however, that overly complex predictive models that consider many variables can also confuse the signal (information that could be useful in creating a prediction) with the noise (meaningless data that obfuscates the trends which could have predictive value).

The Signal and the Noise is divided into two sections. The first section consists of seven chapters, each focusing on a different field of knowledge in which accurate predictions are essential. Silver discusses how modern forecasters have fared in each of these fields, what they got right, and where they went wrong. With meticulous research and an engaging style, Silver takes readers through a journey of the financial crisis of 2008, baseball, basketball, meteorology, seismology, and epidemiology, giving in-depth explanations of how forecasters made predictions and why most of those predictions were astoundingly incorrect. There are, however, a few “success stories.” In particular, Silver points to weather forecasting as a field in which scientists have made incredible progress, using computerized weather models to make forecasts that are much more on target than they could have been a century ago.

The wide range of topics Silver covers inevitably means that most readers will find some of his examples to be more interesting than others. I have little interest in sports, so I found his sections on baseball and basketball to be dull, but I was fascinated by the chapters about weather patterns and earthquakes. Other more financially-minded readers might find the chapter on the 2008 economic crisis to be the most exciting. The nice thing about having so many examples is that every reader, regardless of background, will be drawn in to appreciate the broad implications of Silver’s arguments.

The second section of the book is devoted to Silver’s general approach to being “less wrong” about the predictions we make. In line with his preference for a “foxish” approach, Silver argues that the best way to think about the future is to use a probabilistic method, known as Bayes’s formula. Bayes’s formula is a method to calculate the probability of an event by using both an initial evaluation of the event’s probability and information about new conditions which affect the chances of the occurrence of the event. Bayesian reasoning is a method of constantly updating your knowledge to reflect new circumstances which could change future outcomes.

To illustrate how one would use Bayesian reasoning in a real-life situation, Silver gives us a bit of autobiographical information about the years he spent making money by playing online poker. Probabilistic games, like poker, are good case-studies for Bayesian reasoning because they are relatively simple compared to complex and chaotic systems like the economy or the weather. Silver then shows how one would extend this approach to other areas of prediction, such as anticipating terrorist attacks or analyzing the stock market.

One particularly engaging example of Silver’s methodology is his handling of global warming predictions. The book deals with global warming in a sober and even-handed manner, first acknowledging that there is little doubt behind the theory of global warming: that is to say, there is solid scientific evidence a greenhouse effect triggered by carbon dioxide is causing temperatures to increase, and there is also solid evidence that human production of carbon dioxide is significantly increasing the amount of carbon dioxide in the atmosphere. It is also clear that global temperatures are, on average, warmer than they were a century ago. What can be called into question, though, are specific predictions about how much the Earth will heat up over a given period of time. Silver points out that the stronger the claim one makes about the rise in global temperatures due to global warming, the more susceptible the overall theory becomes to suspicion. For example, if a scientist were to posit that “given that global warming is true, there is only a 15% chance that the next decade will have an average temperature colder than the average temperature in this decade,” and then the next decade is colder than this one, even if we were originally 95% certain that global warming is occurring, by Bayesian probability we would have to update our estimation of the likelihood of global warming down to 85% (assuming that the scientist’s claim was correct). Silver therefore cautions against making such confident claims, encouraging scientists and forecasters of all fields to acknowledge the great amount of uncertainty in complex systems.

The one gripe I personally had with the second section of the book is its failure to fully communicate the mathematics behind Bayes’s theorem. Even though the book is designed for the layman, the proof of Bayes’s formula is relatively straightforward, and it would have made for a better book had Silver taken a few pages to explain where this magical equation comes from. Silver also derided certain aspects of statistics, including statistical significance tests, as being inferior to Bayesian reasoning, and I would have preferred if he had discussed this in a bit more depth. Statistical methods are employed quite frequently in virtually every discipline that involves prediction, and a rejection of those techniques is a bold claim that should warrant a detailed explanation.

Overall, however, the book did an excellent job of accomplishing what it set out to do. Through a myriad of examples, Silver clearly communicates why so many predictions have failed and how he thinks we can try to avoid making similar mistakes in the future. The Signal and the Noise is a book of its time; it is full of political and pop-culture references that would probably be lost to an audience 50 years from now. Despite its contemporariness, though, the book is probably one of the best works out there to explain, in clear and simple English, how to be a critical consumer of the massive quantity of data we have at our disposal in the information age.