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In these notes on Markov Chain Monte Carlo Sampling for Dirichlet Process Mixture Models, page 4, about the middle of the page, they mention that a clustering structure of data phi_1:N is represented by: p(phi_1,....,phi_N)=p(phi_1)p(phi_2|phi_1).........p(phi_N|phi_(1:N-1)) I'm kind of missing how this represents a clustering structure. Thanks |
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This just says that the phi variables have a joint distribution and that the probability of the next phi depends on the probabilities of all the phis that came before. This in itself, as you noticed, does not force a clustering structure on the phis (they could still be independent). However, if you assume the functional form for P presented right above (that says that P(phi_i|phi_1:i-1) is either a draw from g0 or equal to a previously chosen example), then you have a clustering structure. The equation is just saying that all phi variables obey that structure. Ahh ok, I did understand that part, I just was a bit puzzled, since in the text it seems as if that distribution is enough to ensure a clustering structure. Thanks
(Apr 26 '11 at 07:58)
Leon Palafox
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