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Unformatted text preview: stribution is then
p(θy ) = 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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 Spring '12
 CynthiaRudin

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