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Course: CSE 140, Fall 2009
School: UPenn
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best The way to approach a Bayes problem is 1) Determine what the data and hypotheses are. Try to be precise. Data are things that you observe. Hypotheses are things you want to know, but don't observe. 2) What are the prior and the likelihood? P(H|D) = P(D|H) P(H)/P(D) (i) the prior may come from counting previous occurances (frequentist) or from someone's opinion (subjectivist) or...

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best The way to approach a Bayes problem is 1) Determine what the data and hypotheses are. Try to be precise. Data are things that you observe. Hypotheses are things you want to know, but don't observe. 2) What are the prior and the likelihood? P(H|D) = P(D|H) P(H)/P(D) (i) the prior may come from counting previous occurances (frequentist) or from someone's opinion (subjectivist) or from the likelihood principle (see below (ii) likelihoods usually come from a model of the world, but can also be estimated by counting previous occurances. 3) Do you need to find the probability of the data? This is required for finding P(H|D), but not for finding the most likely hypothesis. If you do need to find P(D), is it given, or should it be found by marginalization? P(D) = P(D|h1)P(h1) + P(D|h2)P(h2) + P(D|h3)P(h3) + ... 4) Do you need to make the "Naive Bayes" assumption that data are conditionally independent given the hypothesis? P(d1,d2|H) = P(d1|H)P(d2|H) 5) you Once have estimated the probability of each hypothesis, do you need to make predictions about future data? This generally requires using marginalization. P(newD) = P(newD|h1)P(h1) + P(newD|h2)P(h2) + P(newD|h3)P(h3) + ... where P(newD|H) is the likelihood used above, and P(H) is what was calculated above: P(H | oldD) _____________________________________________________________________________________________ * the likelihood principle states that, in some situations, there are classes of hypotheses, and the prior on a hypothesis is 1/(the number of classes * the...

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