Book Review: The Signal and the Noise

The Signal and the Noise: Why So Many Predictions Fail–But Some Don’t by Nate Silver

Nate Silver runs the FiveThirtyEight website which forecasts American election results, and the (admittedly so far limited) successful track record has shown him to be a deft hand with statistics. I am myself a reader, and so was interested when he came out with a book on the topic of statistics and forecasting and was happily not disappointed.

For whatever reason, one of my great interests is the history of printing, and the introduction of The Signal and the Noise begins with a discussion of the printing revolution (there’s a graph of total book production in Europe on page 3). Maybe I’m just easy, but I was hooked. It was brought up because the total volume of human knowledge is increasing precipitously, which can actually make it more difficult to distill out the really important features.

In terms of subject matter, the book is fairly heavy (in a good way): the causes of the 2008 global recession, political forecasting (obviously his forte), predicting player ability in baseball, weather forecasting (which has shown remarkable improvement over the past few decades), earthquake predictions (in the news recently), economic forecasting (numbers like GDP, unemployment, etc), the spread of contagious diseases, the poker bubble, computer chess (another soft spot for me), attempting to beat the stock market, climate change, and terrorism. The moral of the story is that forecasting and statistics are a serious business.

One of the main conclusions of the book, and why I also listed it under the category of Skepticism, is that there needs to be a more widespread adoption of Bayes’ theorem which deals with how we recalculate certainty in our beliefs when faced with new evidence (this is a running theme in another scientific skeptic circles, such as Science-Based Medicine). That involves assigning a prior probability to our beliefs, which necessarily requires the healthy contemplation of our biases. Bayes’ theorem in a certain notation is

\displaystyle P(A|B) = \frac{P(B|A) P(A)}{P(B)}

read as “the probability of A given B is the probability of B given A times the probability of just A divided by the probability of just B.” Wikipedia has some good examples of it’s use, and I think one of the most famous examples is how even a positive result for some clinical test can still mean that you have a low probability of actual having the disease in question. That it’s conditional, what is the probability of A when we are given B, is the important bit. An example Silver uses in the book is “What is the probability that we’re under a terrorist attack given that a plane just collided into the World Trade Center?” It’s not a slam dunk after the first hit, but given the relatively unlikelihood of the priors of a plane by chance hitting the Towers, when the second plane hit the possibility of it being a deliberate attack rose to very nearly 100%.

Applying Bayes’ theorem to terrorist attacks; that’s how badass this book is. Whatever your fields of interest, it’s likely some of it is covered somewhere in The Signal and the Noise and contains many notes and references (I bought a book about the printing revolution based off the notes).

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