Other words like the will have a high probability

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 03/24/2014 for the course MIT 15.097 taught by Professor Cynthiarudin during the Spring '12 term at MIT.

Ask a homework question - tutors are online