I’ve finally got around to reading Nate Silver’s, The Signal and the Noise, book dealing with predictions. It digs into different areas of business, and the world, people are trying to predict a given event. Nate interviews people in weather forcasting, baseball, seismologists, gambling, stock market, climate change, and politics. Much of the book deals with Bayes’s Theorem, named after Thomas Bayes an English minister born around 1701, which still holds up today. It’s a topic you’ve probably at least heard about if you’ve taken some graduate level courses like an MBA or in your statistics class. They teach the basic equation during the CFA exam. Though I’ve went over the equation a few times, I’ve felt like I’ve had a hard time grasping the details of it to the point where i could recall it on the spot. That’s one of the most beneficial parts of this book. It not only describes Bayes’s Theorem but gives mutliple examples of how people are trying to use this formula in the the real world. It’s driven home the point of how to implement this theorem when dealing with almost any situation whether it’s gambling, terrorist events, cheating boyfriends, or chess tournaments. This theorem is simple yet powerful. We all make predictions on a daily basis. We might not be managing stocks or making million dollar sports bets but we’re deciding the best way to get to work, what should we do with our time, how to handle a situation at work, or whether to buy an item at a particular price. This can all be solved using Bayes’s Theorem.

It’s something you should understand.

See the below breakdown, from Nate Silver’s book, of the different parts of Bayes’s Theorem:

Bayes’s Theorem is concerned with confitional probability. It tells us the probability that a theory or hypothesis is true if some event has happened.

You can answer many questions if you know, or willing to estimate, the below three quantities:

  • Condition of the hypothesis being true: Given new evidence, what is the probability the event did occur?
  • Conditional on the hypothesis being false: Given new evidence, what is the probability the event did not occur?
  • Prior probability: This is your initial estimate of an event happening before you have any new information. Also called, prior.

After estimating the above three values then you can apply Bayes’s theorem to establish a posterior possibility.

  • Posterior possibility is the revised estimate of the event occurring after learning the new information.