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Alejandro1 comments on Open Thread, October 16-31, 2012 - Less Wrong
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hello, all. first post around here =^.^= I've been working my way through the core sequences, slowly but surely, and I ran into a question I couldn't solve on my own. please note that this question is probably the stupidest in the universe.
what is the difference between the Bayesian and Frequentist points of view?
let me clarify: in Eli Yudkowsky's explanation of Bayes' theorem, he presented an iconic problem:
to my understanding of the Bayesian perspective, the answer would be 7.8% and would represent the degree of uncertainty that the subject has breast cancer
to my understanding of the Frequentist perspective, the answer would be 7.8% and would represent the frequency of subjects that both have cancer and tested positive.
a keen observer will understand where my confusion comes from- on my way through the core sequences, I have heard much from the Bayesian side, but nothing from the Frequentist side, making it seem artificially non-existent.
The classical way of explaining the difference is through the example of a coin that you know is biased, but you don't know whether heads or tails is favored and by how much. What is the probability that the next toss will be heads?
Supposedly, a frequentist would say that there is an objective answer, given by the bias of the coin which also equals the proportion of heads in a long run. You just don't know what it is, the only thing you know is that it is not 1/2. A Bayesian would say by contrast that since you have no information to favor one side over the other, the probability (degree of belief) you have to assign at this point is 1/2.
This only explains the question of Frequentism vs Bayesianism as philosophical interpretations of "what probability is". The practical issue of Frequentism vs Bayesianism as concrete statistical methods is often tangled with this one in discussions, but it is really a separate matter.