MIT15_097S12_lec15

The prior is the knowledge part one could interpret

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Unformatted text preview: l be θM L = 1, which predicts that we will never flip tails! How­ ever, we, the modeler, suspect that the coin is probably fair, and can assign ˆ α = β = 3 (or some other number with α = β ), and we get θM AP = 3/5. Question How would you set α and β for the coin toss under a strong prior belief vs. a weak prior belief that the probability of Heads was 1/8? For large samples it is easy to see for the coin flipping that the effect of the prior goes to zero: ˆ ˆ lim θMAP = lim θML = θtrue . m→∞ m→∞ Why? Recall what know about regularization in machine learning - that data plus knowledge implies generalization. The prior is the “knowledge” part. One could interpret the MAP estimate as a regularized version of the ML estimate, or a version with “shrinkage.” Example 1. (Rare Events) The MAP estimate is particularly useful when dealing with rare events. Suppose we are trying to estimate the probabil­ ity that a given credit card transaction is fraudulent. Perhaps we...
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