Bayes' Rule is central for applications of personal probability. It offers a way to represent rational change in belief, in the light of new evidence.
BAYES' RULE
Bayes' Rule is of very little interest when you are thinking about frequency-type probabilities. It is just a rule. On page 70 we derived it in a few lines from the definition of conditional probability.
For many problems–shock absorbers, tarantulas, children with toxic metals poisoning, taxicabs–it shortens some calculations. That's all.
But Bayes' Rule really does matter to personal probability, or to any other belief-type probability.
Today, belief-type probability approaches are often called “Bayesian.” If you hear a statistician talking about a Bayesian analysis of a problem, it means some version of ideas that we discuss in this chapter. But there are many versions, ranging from personal to logical. An independent-minded Bayesian named I. J. Good (see page 184) figured out that, in theory, there are 46,656 ways to be a Bayesian!
HYPOTHESES
“Hypothesis” is a fancy word, but daily life is full of hypotheses. Most decisions depend upon comparing the evidence for different hypotheses.
Should Albert quit this course? The drop date is tomorrow. He is a marginal student and has done poorly so far. Will the course get harder, as courses often do? (Hypothesis 1) Or will it stay at its present level, where he can pass the course? (Hypothesis 2)
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