The core of Bayesian thinking (or Bayesian updating, as it can be called) is this: given that we have limited but useful information about the world, and are constantly encountering new information, we should probably take into account what we already know when we learn something new. As much of it as possible. Bayesian thinking allows us to use all relevant prior information in making decisions. Statisticians might call it a base rate, taking in outside information about past situations like the one you’re in.
Consider the headline “Violent Stabbings on the Rise.” Without Bayesian thinking, you might become genuinely afraid because your chances of being a victim of assault or murder is higher than it was a few months ago. But a Bayesian approach will have you putting this information into the context of what you already know about violent crime. You know that violent crime has been declining to its lowest rates in decades. Your city is safer now than it has been since this measurement started. Let’s say your chance of being a victim of a stabbing last year was one in 10,000, or 0.01%. The article states, with accuracy, that violent crime has doubled. It is now two in 10,000, or 0.02%. Is that worth being terribly worried about? The prior information here is key. When we factor it in, we realize that our safety has not really been compromised.
The first flaw is perspective. We have a hard time seeing any system that we are in. Galileo’ had a great analogy to describe the limits of our default perspective. Imagine you are on a ship that has reached constant velocity (meaning without a change in speed or direction). You are below decks and there are no portholes. You drop a ball from your raised hand to the floor. To you, it looks as if the ball is dropping straight down, thereby confirming gravity is at work.
Now imagine you are a fish (with special x-ray vision) and you are watching this ship go past. You see the scientist inside, dropping a ball. You register the vertical change in the position of the ball. But you are also able to see a horizontal change. As the ball was pulled down by gravity it also shifted its position east by about 20 feet. The ship moved through the water and therefore so did the ball. The scientist on board, with no external point of reference, was not able to perceive this horizontal shift.
This analogy shows us the limits of our perception. We must be open to other perspectives if we truly want to understand the results of our actions. Despite feeling that we’ve got all the information, if we’re on the ship, the fish in the ocean has more he can share.