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I have a question regarding LDA (Latent Dirichlet Analysis) - what is the correct formulation of the posterior? In http://www.cs.princeton.edu/~blei/papers/Blei2011.pdf‎ it is $p(\beta_{1:K}, \theta_{1:D}, z_{1:D} | w_{1:D}) = \frac{p(\beta_{1:K}, \theta_{1:D}, z_{1:D}, w_{1:D})}{p(w_{1:D})}$, but in http://www.cs.princeton.edu/~blei/papers/BleiNgJordan2003.pdf and http://www.cs.princeton.edu/~blei/papers/BleiLafferty2009.pdf‎ it looks different. I would be very grateful if someone could explain me where do these differences come from.

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  • $\begingroup$ Define "correct formulation". There is not such thing. There may be multiple formulations of the same problem. So be more specific about where exactly you have problems understanding the differences. $\endgroup$
    – Has QUIT--Anony-Mousse
    Aug 3, 2013 at 16:12
  • $\begingroup$ The definition of posterior from en.wikipedia.org/wiki/Posterior_probability looks different than those mentioned in the articles. I don't really understand, where does the nominator $p(\beta_{1:K}, \theta_{1:D}, z_{1:D}, w_{1:D})$ come from. I would be also very grateful for a possibly simple explantation, why $p(w_{1:D})$ cannot be computed. $\endgroup$
    – user1315305
    Aug 3, 2013 at 17:15
  • $\begingroup$ Looking different doesn't mean it is mathematically different. People use different notations, and specialize formulas for different prior assumptions. p(w_{1:D}) probably cannot be computed because you don't have enough data to get a statistically sound value. Don't assume independence! $\endgroup$
    – Has QUIT--Anony-Mousse
    Aug 3, 2013 at 17:21

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