Driven by data; ridden with liberty.
Prediction is both an art and a science. Recent history is littered with catastrophic failures of prediction, from grave underestimates of mortgage defaults in the United States, to unsubstantiated claims about political elections. In these uncertain times, Nate Silver seeks to help the reader with his book The Signal and the Noise.
Silver sees people demarcated into two broad categories: ‘foxes’ and ‘hedgehogs’. This is borrowed from a passage attributed to the Greek poet Arichilochus (pg. 53): “The fox knows many little things, but the hedgehog knows one big thing.” Silver states that due to their empirical, cautious and multi-disciplinary nature, foxes make better forecasters. Hedgehogs make better television guests, but foxes may not succeed in politics, as (pg. 56):
Their belief that many problems are hard to forecast – and that we should be explicit about accounting for these uncertainties – may be mistaken for a lack of self-confidence. Their pluralistic approach may be mistaken for a lack of conviction.
After surveying the problems and principles of prediction, Silver treads an autobiographical tale of his life’s journey. As a fan of baseball – a game which had “the world’s richest data set” (pg. 79) – Silver began developing PECOTA, which sought to identify great players, through separating skill from luck, and determining the aging curve of player performance. The author then moves to weather forecasting. The weather is a dynamic and non-linear system, meaning the system’s behaviour at one point affects its behaviour in the future, and its build upon exponential – rather than additive – relationships. Chaos theory is the branch of mathematics that studies dynamic and non-linear systems. The fact that the weather and economics “continually evolve in a chain reaction of events is one reason it is very difficult to predict” (pg. 118—119).
The human desire for crystalline predictions in a chaotic world often leads to misguided claims. As Silver notes (pg. 145):
When catastrophe strikes, we look for a signal in the noise – anything that might explain the chaos we see all around us and bring order to the world again.
Earthquake predictions can involve ‘over-fitting’: “the name given to the act of making noise for a signal” (pg. 163). When a model is overly specific and matches the limited data too closely, this means further extrapolations will be more prone to failure. Silver calls over-fitting “the most important scientific problem you’ve never heard of”.
One chapter examines Bayes’ Theorem. It was fun to see this theorem, which is mathematically simple but philosophically rich, appearing in a popular book. Bayes’ Theorem calculates the probability of an event given another event has taken place. This theorem helps explain why false positives dominate mammogram results.
After considering traditional problems, Silver turns his hand to computerised chess, Texas Hold ‘Em Poker and terrorism. It is a fascinating and engaging read, with Silver guiding the reader through some fairly difficult concepts with relative ease. This book is great for budding statisticians, or for anyone interested in the enigmatic and empirical nature of our world.