There have been two fundamentally different approaches to probability. One emphasizes the frequency idea. The other emphasizes the belief idea.
Some theorists say that only one of those two ideas really matters. We will call them dogmatists. In this book we are eclectic. Here are two definitions taken from a dictionary:
♦ Eclectic. Adjective. 1. (in art, philosophy, etc.) Selecting what seems best from various styles, doctrines, ideas, methods, etc.
♦ Dogmatic. Adjective. 1. Characterized by making authoritative or arrogant assertions or opinions, etc.
FREQUENCY DOGMATISTS
Some experts believe that all inductive reasoning should be analyzed in terms of frequency-type probabilities. This is a dogmatic philosophy, saying that inductive reasoning should rely on exactly one use of probability. Belief dogmatists often say that frequency-type probabilities “have no role in science.”
BELIEF DOGMATISTS
Some experts believe that all inductive reasoning should be analyzed in terms of belief-type probabilities. This is a dogmatic philosophy, saying that inductive reasoning should rely on exactly one use of probability. Belief dogmatists often say that frequency-type probability “doesn't even make sense.”
OUR ECLECTIC APPROACH
Chapters 16–19 and 22 use the frequency idea. Chapters 13–15 and 21 use the belief idea.
Luckily, most (but not all) data and arguments that a frequency dogmatist can analyze, a belief dogmatist can analyze too. And vice versa. Only in rather specialized situations do the two schools of thought draw really different inferences from the same data.
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