The Bayes theorem, explained to an above-average squirrel

Editor’s Note: The following question was recently asked of our statistical training instructors. Terry Woodfield, along with Bob Lucas took the time to write this eloquent and easily digestible answer.

Question: I’m trying to get a general – very general – understanding what the Bayes theorem is, and is used for. Can anyone give me a simple definition of the Bayes theorem – and by simple I mean really simple, like if you were trying to explain it to an above-average squirrel.

Maybe a fill in the blank thing, like this:

The Bayes theorem (horribly dumbed-down) is…
It’s very useful in situations like these…
It’s a great choice to use in these situations because…

Answer: Here is my take on Bayes theorem. In life, almost everything is “conditional.” I can ask, “What is the life expectancy of a Caucasian male?” The answer may be something like 72 years. However, I am 54 years old, so a better question for me is, “What is the life expectancy for Caucasian males that have survived 54 years?” The answer will almost certainly be larger than 72. I want an estimate “conditioned on” the fact that I have already lived 54 years. Life is dynamic. Things are constantly changing. However, too often decisions are based on static information. Bayes theorem takes advantage of dynamic information to give a better, more correct answer.

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