(This article was originally published at Normal Deviate, and syndicated at StatsBlogs.)

**Nate Silver Is A Frequentist**

**Review of “the signal and the noise” by Nate Silver**

There are not very many self-made statisticians, let alone self-made statisticians who become famous and get hired by the New York Times. Nate Silver is a fascinating person. And his book the signal and the noise, is a must read for anyone interested in statistics.

The book is about prediction. Silver chronicles successes and failures in the art of prediction and he does so with clear prose and a knack for good storytelling.

Along the way, we learn about his unusual life path. He began as an economic consultant for KPMG. But his real passion was predicting player performance in baseball. He developed PETOCA, a statistical baseball analysis system which earned him a reputation as a crack forecaster. He quit his day job and made a living playing online poker. Then he turned to political forecasting, first at the Daily Kos and later at his own website, FiveThirtyEight.com. His accurate predictions drew media attention and in 2010 he became a blogger and writer for the New York Times.

The book catalogues notable successes and failures in prediction. The first topic is the failure of ratings agencies to predict the bursting of the housing bubble. Actually, the bursting of the bubble was predicted, as Silver points out. The problem was that Moody’s and Standard and Poor’s either ignored or downplayed the predictions. He attributes to failure to having too much confidence in their models and not allowing for outliers. Basically, he claims, they confused good “in-sample prediction error” as being the same as “good out-of-sample prediction error.”

Next comes a welcome criticism of bogus predictions from loud-mouthed pundits on news shows. Then, a fun chapter on how he used relatively simple statistical techniques to become a crackerjack baseball predictor. This is a theme that Silver touches on several times. If you can find a field that doesn’t really on statistical techniques, you can become a star just by using some simple, common sense methods. He attributes his success at online poker, not to his own acumen, but to the plethora of statistical dolts who were playing online poker at the time.

He describes weather forecasting as a great success detailing the incremental, painstaking improvements that have taken place over many years.

One of the striking facts about the book is the emphasis the Silver places on frequency calibration. (I’ll have more to say on this shortly.) He draws a plot of observed frequency versus forecast probability for the National Weather Service. The plot is nearly a straight line. In other words, of the days that the Weather Service said there was a 60 percent chance of raining, it rained 60 percent of the time.

Interestingly, the calibration plot for the Weather Channel shows a bias at the lower frequencies. Apparently, this is intentional. The loss function for the Weather Channel is different than the loss function for the Nation Weather Service. The latter wants accurate (calibrated) forecasts. The Weather Channel wants accuracy too, but they also want to avoid making people annoyed. It is in their best interests to over-predict rain slightly for obvious reasons: if they predict rain and it turns out to be sunny, no big deal. But if they predict sunshine and it rains, people get mad.

Next come earthquake predictions and economic predictions. He rates both as duds. He goes on to discuss epidemics, chess, gambling, the stock market, terrorism, and climatology. When discussing the accuracy of climatology forecasts he is way too forgiving (a bit of political bias?). More importantly, he ignores the fact that developing good climate policy inevitably involves economic prediction, to which he already gave a failing grade. (Is it better to spend a trillion dollars helping Micronesia develop a stronger economy so they don’t rely so much on farming close to the shore, or to spend the money on reducing carbon output and hence delay rising sea levels by two years? Climate policy is inextricably tied to economics.)

Every chapter has interesting nuggets. I especially liked the chapter on computer chess. I knew that Deep Blue beat Gary Kasparov but beyond that, I didn’t know much. The book gives lots of juicy details.

As you can see, I liked the book very much and I highly recommend it.

But …

I have one complaint. Silver is a big fan of Bayesian inference, which is fine. Unfortunately, he falls into that category I referred to a few posts ago. He confuses “Bayesian inference” with “using Bayes’ theorem.” His description of frequentist inference is terrible. He seems to equate frequentist inference with Fisherian significance testing, most using Normal distributions. Either he learned statistics from a bad book or he hangs out with statisticians with a significant anti-frequentist bias.

Have no doubt about it: Nate Silver is a frequentist. For example, he says:

**“One of the most important tests of a forecast — I would argue that it is the single most important one — is called calibration. Out of all the times you said there was a 40 percent chance of rain, how often did rain actually occur? If over the long run, it really did rain about 40 percent of the time, that means your forecasts were well calibrated.”**

It does not get much more frequentist than that. And if using Bayes’ theorem helps you achieve long run frequency calibration, great. If it didn’t, I have no doubt he would have used something else. But his goal is clearly to have **good long run frequency behavior**.

This theme continues throughout the book. Here is another quote from Chapter 6:

**“A 90 percent prediction interval, for instance, is supposed to cover 90 percent of the possible real-world outcomes, … If the economists’ forecasts were as accurate as they claimed, we’d expect the actual value for GDP to fall within their prediction interval nine times out of then …”**

That’s the definition of frequentist coverage. In Chapter 10 he does some data analysis on poker. He uses regression analysis with some data-splitting. No Bayesian stuff here.

I don’t know if any statisticians proof-read this book but if they did, it’s too bad they didn’t clarify for Silver what Bayesian inference and frequentist inference really are.

But perhaps I am belaboring this point too much. This is meant to be a popular book, after all, and if it helps to make statistics seem cool and important, then it will have served an important function.

So try not to be as pedantic as me when reading the book. Just enjoy it. I used to tell people at parties that I am an oil-fire fighter. Now I’ll say: “I’m a statistician. You know. Like that guy Nate Silver.” And perhaps people won’t walk away.

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