Many readers of this column will never have heard of Bayes’ Theorem or Bayesian inference. The latter has sparked years of debate among statistical researchers and is evidently making a comeback in how widely it is used. This debate presents several issues that are not only interesting but relate to highly pragmatic concerns that many people should find useful.
Thomas Bayes was an 18th century minister from England who developed one of the basic principles of probability. It is a simple mathematical formula (that I will forego writing down) that shows how the probability of a random event occurring is modified when partial information relevant to the event is obtained and considered. If I am in a casino playing roulette, there are 38 equally probable slots into which to ball can fall (1 through 36, 0 and 00). If I have a bet on number 10, my probability of winning is 1/38th (about 2.6 percent). Now suppose that the ball falls and initially I can’t see the number, but I can see that it has landed in a red slot. (Even numbers are red, odd numbers are black, 0 and 00 are green.) Now there are only 18 slots into which the ball could have fallen. Since 10 is a red slot and is still in the running, my probability of winning is now 1/18 (about 5.6 percent). Knowing that the ball landed in a red slot has modified my probability of winning, more than doubling the chance for success.
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