by David Siegel
In contrast to Extremistan, Bayesian reasoning relies on the power of the average as a driving force in many areas of life. My goal here is to present an overview of Bayesian reasoning and let you explore deeper as time allows. Soon, you will understand Bayesian reasoning, and it will change you forever.
The essence of Bayesian reasoning is that we should take into account what we already know about something before we analyze a particular situation. Thus, if someone says she's going skydiving and you're concerned about her safety, you should ask questions about how she will get there, how long the trip will take, who's driving, what shape the car is in, traffic, etc. If you hear of another tragic school shooting, and the shooter's name, life, and photos are all over the press and the shooter is an instant celebrity, you can assume there will be another shooting some months later, no matter what people in law-enforcement or government do. If you go to a casino, sit at a $5 blackjack table, and play the optimum strategy, you can expect to lose $3 per hour. If you invest in a hedge fund or mutual fund that has outperformed its peers in the past five years, you can expect it to underperform in the next five. If God has ever answered one of your prayers, you now know how datamining works. A Bayesian outlook requires us to use evidence to see what is most likely to be true and what isn't, so we can be less wrong in our assumptions. And, studies show that only 15% of doctors can answer Bayesian problems properly. We have a long way to go.
Facts vs Evidence
Facts are readily available. You can always find a fact to support your argument. The problem with facts is that they tend to distort rather than clarify the picture. Anyone who has won an argument has called forth a number of specific facts, while leaving others out. And, facts tend to be less true as time goes on - the facts of ten years ago are less factual today than they were then. Evidence is different. Evidence is everything. You can't remove evidence, you have to incorporate it. This makes the picture much more complicated. People who work with evidence look for trends but often find that there are exceptions and puzzling cases that just don't fit. People who work with evidence often use scatter plots, rather than trend lines. For an excellent introduction to an evidence-based approach, read The Signal and the Noise: Why So Many Predictions Fail But Some Don't, by Nate Silver.
Stories vs Evidence
According to several popular business books, back in the mid-1980s a man walked into a Fairbanks, Alaska, Nordstrom store and returned a pair of tires. Despite the fact that Nordstrom doesn't sell tires, the manager took back the tires and gave him the price marked on them. This story has been worth its weight in gold for Nordstrom, as it has been retold many times by the press and elaborated on in various versions. However, the evidence against this story is convincing. That hasn't stopped Nordstrom from using it to help build its reputation.
Stories are powerful. Our decision processes are often hijacked by people telling stories and using emotion to convince us. Anecdotes are not evidence, but they grab the emotions and easily convince people of general themes. The human brain is designed to use stories to remember, simplify, and understand our complex world. But stories never tell the whole story, and stories mislead us more often than not.
Bayesian reasoning is based on evidence. As new evidence comes in, we change our outlook and may make different decisions. People who are adept at Bayesian reasoning are called foxes - they make many small decisions and continually adjust their view of the world as new evidence comes in. Even though you may think you know and use these principles, there are people who are way ahead of you. They are enthusiastic about communicating what they know, but it takes time and effort to learn. One such person is Eliezer Yudkowsky, whose writings and the community he has built at LessWrong.com are brilliant points of light shining through the fog, with plenty of material for learning Bayesian reasoning. If you have read the Harry Potter series, you will love his epic work of fanfiction, Harry Potter and the Methods of Rationality (warning - it could take you a few weeks to get out of there once you fall in). You'll find a selection of Bayesian and statistical links on our Resources page.
The Best of Both Worlds
It is possible to combine a Bayesian view of the world with a black-swan view, in which we are skeptical of claims and theories and adjust our decisions as we get new information, while we are hedged and prepared for future unforeseen events that will have extreme consequences, both good and bad. Can you benefit from having Bayesians, statisticians, portfolio specialists, and decision-scientists on your team?
To get started, see What We Do.