Predicting the Future Is Hard

Building better models, from elections to financial markets


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. 

Human judgment enables a model to reflect human information, but it also introduces the potential for bias from using our perception to build models and interpret their results. This inclination can sometimes be a feature, as in weather prediction's improvements over time by searching for and testing for patterns, or a bug, as in cases like finance and baseball, where bias can lead to less accurate prediction.

Some of Silver's chapters cohere with the central Bayesian theme better than others do, and Silver does not consistently maintain the distinction between risk and uncertainty. Still, his skillful writing and storytelling make The Signal and the Noise an enjoyable read, even if you are not a prediction junkie. Overall it is a thoughtful, well-cited work with informative attention to detail.

Similarly, James Owen Weatherall's The Physics of Wall Street is an engaging, well-written history of the work of physicists, mathematicians, and statisticians on modeling financial markets since the late 19th century. Weatherall, a physicist, mathematician, and philosopher, unearths research from some unjustifiably underappreciated mathematicians, and he narrates a lively story about their work while making challenging ideas easier to understand.

Some of Weatherall's subjects, such as Benôit Mandelbrot, discovered entirely new fields of inquiry (in Mandelbrot's case, fractal geometry and chaos theory) as they developed theories to solve concrete problems. Others, such as physicist Fischer Black, pioneered the application of physics models to complicated finance problems like options pricing. In all cases Weatherall shows that intellectual nonconformity and interdisciplinary collaboration were key to his subjects' successes.

Weatherall's main theme is that the methodology of physics involves developing appropriately simple models, being honest about their assumptions, testing those models, and then revising them based on their performance and/or when the assumptions are invalid. Based on this foundation, he argues that the physicists and other quants are not entirely to blame for failures to predict financial market downturns such as the recent 2008 crisis, nor even for having developed models and financial innovations that made financial markets more brittle and less resilient. 

"Putting all of the blame for the 2007–2008 crisis on Li's model, or even securitized consumer loans, is a mistake," Weatherall writes. "The crisis was partly a failure of mathematical modeling. But even more, it was a failure of some very sophisticated financial institutions to think like physicists. The model worked well under some conditions, but like any mathematical model, it failed when its assumptions ceased to hold."

Weatherall's research and argument are broadly persuasive but incomplete. His account does not address the fact that physicists develop these models within a framework of human institutions, the sets of formal and informal rules that govern how individuals act and interact in financial markets and the broader economy. These institutions shape the incentives of all kinds of people—including quants and the people who employ them—in the complex network of markets. 

So Weatherall's conclusion is accurate, but the financial crisis was largely a failure of institutions and incentives that made financial markets more brittle, not solely a failure of mathematical modeling per se. While the Warren Zevon fan in me appreciates his epilogue's invocation to "send physics, math and money!" to enable better outcomes in financial markets, it's a prescription that overlooks the distorted incentives that existed, and persist, in financial markets.

These two books have several shared attributes that make them worth reading—lively writing that humanizes a difficult topic, attempts to understand modeling and prediction in the face of uncertainty, and application to well-examined case studies in finance, weather, earthquakes, and poker. A common theme is the danger of assuming that the risks of bad outcomes are independent of each other instead of related, especially in financial markets. Having faith that your model will work regardless of conditions leads to poor predictions and unexpected outcomes. Good modeling requires constant testing and humility, even (or especially) after a spectacularly successful election prediction. 

NEXT: Marijuana Cannon Used to Smuggle Pot into the U.S.

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  1. I think Silver lucked up in predicting the elections because of Romney’s 47% comment, the storm (seeing government in action fixing things, Christie and Obama together, reminder of global warming), and a few other factors. Of course: the economy was showing signs improving slightly over a few years, in today’s environment there is a severe distrust of rich people.

    1. It is also worthy of noting that since the election, it has been revised to reveal that Obuma barely won the national election (due to the discovery of huge voter fraud in my loathsomely purple home state of Ohio). The popular vote has been revised to 51/49.

      I think Nate Silver got lucky, I think Romney should have blown this bozo out of the water (in the absence of that “47%” comment in a room full of evul rich), and the screaming elephant in the room is: why the fuck does California have twice as many electoral votes as Texas? This question has to be put out on the national stage, because it allows a democrat to win the national election by taking a small handful of states.

      1. California population: 38,041,430
        Texas population: 26,059,203

        California EVs: 55
        Texas EVs: 38

        Population ratio: 1.46
        EV ratio: 1.44

        1. But surely the fact that those numbers balance out quite fairly is just me having a good day. Tomorrow the nature of numbers will most certainly be different and my luck won’t be so good.

          1. Tomorrow California will collapse like every other collectivist “utopia”, that might be just the kick in the ass America needs to start rejecting your backwards-ass “progress”.

            You’ll also notice that anyone worth a fuck is fleeing the bankrupt sewer of California, and I will not be surprised when it turns out that the population numbers had been fudged all along.

            Don’t lecture me about “numbers”, you fucking faggot–the ability to manipulate numbers does not change the basic nature of reality, as you and your ilk will soon discover.

            1. You’re making Tony look reasonable with your hyperbole and name-calling.

              And people are fleeing at the margins, not wholesale — California neither gained nor lost EVs in the last reapportionment, which means its population growth roughly mirrored the national average.

          2. Huhn. States with large populations having more EVs than states with smaller populations?

            What a shocker.

            1. The population numbers are fudged. Nobody could possibly want to live in a coastal state with a yearlong temperate climate and perfect abs and breasts galore when they could go to fucking Texas and chaw on something.

              1. California has good weather and horrendous governance, Texas has pretty good governance and crap weather.

                Result? California treading water on population, Texas gaining four EVs.

                I suspect that unless the governance in CA improves, the next census will cause them to lose EVs.

                1. Some companies have moved from California to Texas, and including that, the main reason for California’s small decline in population is its high cost of living. And the overwhelming factor in Texas’s population growth is the growth of its Hispanic population.

                  I predict Texas will turn blue before California collapses into a socialist sinkhole. And it’s pretty easy to be propped up as a success story of capitalism when you happen to be sitting on heaps of one of the world’s most important natural resources.

      2. I started to say that Romney was the worst possible choice and then I thought of all the other horrible candidates whom I would have never chosen. What a shitty field of candidates. With a bad economy, Obama should have lost but somehow that did not count this time.

  2. The litmus test for Nate Silver will be how well his predictions do in retrospect when a Republican wins the Presidency. I think his predictions lean to the left. As long as the trend is left he’ll do very well, if the trend is right will his predictions be as good? Only time will tell.

    1. If Silver’s predictions leaned to the left, he would have predicted Obama winning some states he lost.

      Silver seems to have a pretty decent model. There is certainly room for improvement — he didn’t call the exact percentages of victory in each state — but it is a proven rough predictor of what is likely to happen.

      1. A good point.

  3. The only surprise for me election night was Obama winning Florida, so I don’t understand why people are acting so amazed at Nate Silver.

    Also, unless you’re planning and making decisions differently based on the outcome, how useful is this prediction to you? Unless you’re heavily involved in high-level policy, law, and lobbying, what did you do with the knowledge that Obama was likely to win?

    I’m more interested in predicting the stock market than which asshole is going to be holding a veto pen for the next four years.

    1. so I don’t understand why people are acting so amazed at Nate Silver

      Because everyone else calling it was making predictions not in touch with objective reality, including blowhards here saying it would be a blowout for Romney or Obama, instead of the fairly close thing it was hinging on a few swing states won by a small percentage?

      Perhaps you should be running a competing prediction model if you think Silver’s model is not precise enough.

      1. Because everyone else calling it was making predictions not in touch with objective reality, including blowhards here saying it would be a blowout for Romney or Obama, instead of the fairly close thing it was hinging on a few swing states won by a small percentage?

        I won money on the election betting against my stupid friends who said Romney was going to win. If Nate Silver is a genius primarily because of how stupid other people are, I’m still not impressed.

        Perhaps you should be running a competing prediction model if you think Silver’s model is not precise enough.

        To me, it seems a waste of time to go into complicated modeling, when my quick estimate of the result was already within 29 electoral votes of the outcome. However, I do have a background in statistics. Maybe I could start blogging like Nate Silver, and maybe, run my own webpage and become a politicial analysist. That way, I can make money telling people the outcomes of events that they will surely become aware of with absolute certainty, as long as they live past the election day. If I don’t die of boredom first.

        There’s plenty of money to be made engaged in activities that I find much more preferrable. I’ll pass.

  4. Mandelbrot Set

    Just leaving this here for shits and giggles.

  5. Another review of Weatherall.

    1. Thanks that was interesting and fun to read people letting him have it.

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  11. the fact that our pattern-based predictions were incorrect, and we update

  12. fact that our pattern-based predictions were incorrect,

  13. fact that our pattern-based predictions were incorrect

  14. recognition and our inherent biases, how do we separate

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