MIT15_097S12_lec15

Other words like the will have a high probability

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Unformatted text preview: stribution is then p(θ|y ) = θmH (1 − θ)m−mH 2 1/2 'm θ H (1 0 − θ' )m−mH 2dθ' . The partition function is an incomplete Beta integral, which has no closed form but can easily be solved numerically. In the following figure, we draw samples iid from the true distribution (3/4 probability of Heads) and show how the posterior becomes increasingly concentrated around θ = 0.5, the closest likelihood function to the true generating distribution. 5 Hierarchical modeling Hierarchical models are a powerful application of Bayesian analysis. They al­ low us to reason about knowledge at multiple levels of abstraction. Basically, 19 the prior parameters at the lower level come from the same distribution at the higher level, and there is a prior at that level, and so on. This is best explained by example, so we will develop a hierarchical model for topic mod­ eling, an important information retrieval problem. 5.1 Topic models Suppose we have been given a collection of m documents and we wish to determine how...
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