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This was just a thought that occurred to me, but technically, is it possible to redefine what I treat as latent variables and what I treat as data?

For example, lets assume I have a set of latent variables that can describe 2 datasets equally well (but datasets origin form 2 different distributions). Now I am interested what part of my latent variables is better associated with which distribution. Could I simply treat those latent variables as my dataset, and the distributions as my latent variables?

or in general, if I have a likelihood p(y|z) (described by some gaussian distribution) computed using some model. If I change my problem statement could I redefine this likelihood to be a posterior?

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  • $\begingroup$ If variables are latent, it means they are not observed so your proposal is unclear. Latent variables can be treated as parameters, instead. $\endgroup$ – Xi'an Feb 21 at 7:27
  • $\begingroup$ I predicted those latent variables using another model and then treat them as observables. If that makes sense $\endgroup$ – SandraK Feb 21 at 7:31
  • $\begingroup$ I would rather aggregate both models rather than using plugg-in as a proxy to the latent variables. $\endgroup$ – Xi'an Feb 22 at 21:16

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