The Signal and the Noise: Why So Many Predictions Fail—But Some Don’t, by Nate Silver, Penguin Press, 544 pages, $27.95
The Physics of Wall Street: A Brief History of Predicting the Unpredictable, by James Owen Weatherall, Houghton Mifflin, 304 pages, $27
Human beings naturally look for patterns in the mess of events and data that surrounds us. Groping for hidden architecture is an evolutionary response to a complex world. In general it serves us well, but we risk detecting patterns where none actually exist.
Sometimes we can learn after the fact that our pattern-based predictions were incorrect, and we update and move on, ideally with more humility and an updated mental model for the future. But biases often persist even after correction, especially when the subject of our attention is something with deep emotional roots, like the predicted outcome of an election.
Given the power of pattern recognition and our inherent biases, how do we separate the signal from the noise? That question has intrigued statisticians for centuries, including the statistician of the moment, Nate Silver. In The Signal and the Noise, the well-known New York Times poll-watcher examines the phenomenon of prediction. Silver asks how, in the face of uncertainty, we can separate meaningful patterns from the vast amount of information and data available to us.
Our innate cognitive limitations and biases, the biases arising from our use of perception, and the biases we introduce into prediction due to our interpretation and analysis all combine to distort rather than clarify. As Yogi Berra once observed, “Prediction is very hard, especially about the future.”
Prediction involves a theoretical model to formulate a hypothesis, an empirical model to gather and analyze the (necessarily incomplete) data to test that hypothesis, and a method of evaluating the inferences drawn from those models to see if the theoretical and empirical models can be improved, in order to generate better future predictions.
Silver argues that better models and more successful predictions come from applying Bayesian reasoning, which revolutionized statistics in the 18th century and is used in engineering, medicine, and economics to analyze data. Bayesian reasoning involves formulating a probability of an event’s occurrence, then updating that probability as new data arrive. Silver uses the example of finding a strange pair of underwear in your partner’s drawer. A Bayesian analysis of whether your partner is cheating on you requires a hypothesis (cheating), an alternative hypothesis or reason why the underwear would be there, and a prior probability you would have assigned to the cheating hypothesis before finding the underwear. This prior is crucial. Given estimates of these variables, you can calculate an estimate of the probability that your partner is cheating on you, which you can express as a degree of confidence in the cheating hypothesis.
A fundamental Bayesian insight is that we learn about the world (and its patterns) incrementally. As we gather more data, says Silver, we get “closer and closer to the truth” (emphasis in original). Thus we can refine our models and perform better approximations, yielding more accurate estimates of our confidence in the truth of the hypothesis.
Silver has applied these techniques in formulating statistical models in poker, in baseball, and most famously in U.S. presidential elections. (In 2008 he accurately predicted the outcome in 49 out of 50 states. In 2012 he was right about all 50.)
The Bayesian approach to probability and statistics is not the only one, and it is not always intuitive. The largest debate in probability theory arises between the Bayesian and the frequentist approaches. Frequentists interpret the probability of an event as a relative frequency of its occurrence, which is defined only in reference to a base set of events (for example, the probability of heads in a large number of coin tosses). In Bayesian statistics, a probability is a subjective degree of confidence based on a subjective prior, so each person can hold a different probability of the same event occurring. That subjectivity means abandoning the idea of probability as a frequency.
However esoteric this debate sounds, it’s at the core of the different interpretations of Silver’s 2012 U.S. presidential predictions. He chose as his subjective prior a set of state-level polls that in his judgment were more likely to represent underlying beliefs accurately, and therefore enable him to make predictions more accurately.
But by and large, people find frequentist representations more intuitive. Research from the psychologist Gerd Gigerenzer, supported by further evolutionary psychology research by Leda Cosmides and John Tooby, indicates that we tend to apply more accurate Bayesian reasoning when presented with probabilistic data in frequency form. Gigerenzer’s pioneering research also shows how we use heuristics and rules of thumb to make approximations in complex situations when we cannot grasp all of the data relevant to a decision.
Silver contends correctly that such trial-and-error intuition contributes to the biases that can harm prediction, but he does not discuss the fundamental and important tradeoff that exists between the costs of those biases and the benefits that arise from informed approximation. Bayesian reasoning is itself a rule of thumb, and one that encourages us to be more systematic in our thinking about the future.
Silver develops his theme in application to several case studies told as freestanding vignettes, from political prediction to sports betting to climate. Predictions in these cases have differing degrees of success, depending on the quality of the theoretical and empirical models, as well as the availability and reliability of the data with which to test them. The quality of models depends on variables such as computing technology and how nonlinear and dynamic the underlying system is. It also depends on the judgment of the person constructing the model.