Reverend Bayes can save the world 
[Sep. 2nd, 200802:53 am]
Arvind Narayanan

My advisor once said to his undergrad CS class that if they were to remember only one equation from their four years of college education, it should be Bayes' rule. I couldn't agree more: in fact, I think it's the most important equation you can learn in life.
Most readers of this blog already know what Bayes' rule is. For the rest of you, I won't bore you with math, but here's an example: let's say one in a million people on the streets are out to mug you at any given time, and that thugs are ten times more likely to wear a hoodie than nonthugs. If you see a suspicious looking guy in a hoodie coming toward you, the chance that you're going to get mugged is still only 1 in a hundred thousand. Not worth breaking into a sweat over.
That's a simple (and somewhat extreme) example, but our everyday lives are full of situations where a dose of Bayesian reasoning can greatly clarify the picture. Most intellectual jobs heavily involve Bayesian reasoning as well: disease diagonis is a rather wellknown example. (Here's a hint: House is probably the most statistically unlikely TV show ever.) And apparently, only 15% of doctors are capable of basic Bayesian logic. The next time you hear one of those horror stories of repeated incorrect diagnosis, you know why.Usually, only around 15% of doctors get it right... See Casscells, Schoenberger, and Grayboys 1978; Eddy 1982; Gigerenzer and Hoffrage 1995; and many other studies. It's a surprising result which is easy to replicate, so it's been extensively replicated.) If you manage to internalize Bayes' rule, it feels like your IQ just jumped up 20 to 30 points, and the world looks different. Notice that I said internalize  that's very different from learning the formula. It's roughly the difference between learning Newton's laws of motion and being able to duck in time when a baseball is thrown at your face.
By some fluke, I managed to discover and internalize Bayes' rule some time when I was a kid. I didn't know what it was called, of course, and I didn't know I knew something other people didn't. When they finally taught it in school, my reaction was "this actually has a name?!" rather than "wow!". The downside is that I used to wonder if there was some kind of elaborate joke that I wasn't in on  such as when people would take a perfectly normal event and decide en masse to designate it a "miracle."
Going back to the guyinahoodie example, imagine feeling no discomfort in that situation. Or being completely unaffected by the fearmongering in the media (whether it's terrorism, climate change, or something else.) Or being able to make rational investments. It can definitely feel like a superpower at times. Not only do you make much better decisions, you are far less stressed about them. I love the tongueincheek term "Bayesattva" (a pun on Bodhisattva) from Yudkowsky's* very long but excellent tutorial on Bayes' theorem.
The inability to use Bayesian reasoning (more precisely, to take priors into account) is what people mean when they say that humans are terrible at probabilities. But if you bite the bullet and decide to digest Bayes' theorem, you'll be smarter, richer, happier, have more empathy, and a better sex life. (OK, I may have made that last one up :)
*Eliezer Yudkowsky, the sixth smartest person to have lived in the last 100 years, after Turing, Von Neumann, Einstein, Witten and Tao. 

