One of my favorite theorems is Bayes' theorem. (There, I admit it. I'm a geek.) At its heart, Bayes' theorem is a way to update a probability estimate with new information. Say for instance you hear that there is a one in ten chance of rain today. Later on, you see some ominous clouds. It's reasonable to think that the probability is now a bit higher in light of this new observation. But yet the original ten percent forecast still has some value. Bayes' theorem calculates the updated probability based on the original ten percent forecast, the chance of ominous clouds showing up independent of any forecast of rain, and finally the probability of ominous clouds on days that it really does rain. Frankly, you don't have to have the precise formulation memorized to make some of it. The Wikipedia link above is good enough if you want to dive in a little bit deeper.

I first encountered Bayes' theorem in graduate school. One of the atomic physics grad students who had gotten his PhD a couple of years earlier came back to talk about his current work. It was some government job tracking radon in houses. I don't remember exactly how he used Bayesian analysis, but what struck me is that it seemed to be able to create data from nothingness. He had some very sparse data about Radon instances and went on to construct a pretty thorough model of radon concentrations across the country. It retrospect I understand that he took raw data and applied additional knowledge like Gaussian distributions and other assumptions that don't seem like knowledge in themselves but helped extend the base data.

But at the time, something just didn't seem right about it. So I looked into it more. Later on I used it my own research. There was a Bayesian classification algorithm that I found somewhere that would identify clusters of data from a raw, uncorrelated source. My research involved finding optimal structures for silicon clusters and I used this Bayesian classification algorithm to find trends among the vast library of locally stable clusters I found though simulated annealing, Monte Carlo, and genetic search algorithms.

But the title of this post is "The Bayesian approach to life" not "The Bayesian approach to classifying silicon clusters" (Although I think you can still find references to my abortive attempts out there somewhere.) The thing is that Bayes can shine light statistics and probabilities you hear every day. Let's say you hear some expert talking head say there is a 50% chance that Twinkies cure cancer. You might think of this as knowledgeable assessment of the situation. But on the other hand, you see that the expert knows there are two options (cures cancer or doesn't) and he offers no additional insight.

Mostly it's just a nice way to think about uncertainty. Probably in an everyday sense is really about updating estimates based on new evidence. You can't do that right without Bayes. It's also useful when you have to deal with an observation that can have more than one cause.