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This may be a silly question, but I'm not seeing a clear answer in any of the usual sources. I'm preparing to build a Bayesian model to fit with BUGS/JAGS, currently working through the model logic in plate notation.

I have a few kinds of observed variables, and several latent variables. I know that a Bayesian model has to be a DAG. What other conceptual constraints are there on the network? In particular, can an observed variable be the parent of a latent variable in a Bayesian model?

Thanks, and happy fourth of July to all the Americans out there.

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Sure, parents of latent variables can be observed.

The graph just encodes conditional independence relationships among variables, and is totally separate from the question of which variables are observed or latent. For example, if the graph is $X \to Y \to Z$, this tells you that the density $f(x,y,z)$ factors as $f(x) f(y|x) f(z|y)$, but doesn't tell you anything about which variables are observed.

(It can be easier or harder to do inference depending on which variables are observed, though.)

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  • $\begingroup$ Great response, thanks! Any pointers on your last comment? What do you mean by inference that is harder or easier, and what variable structures affect it? $\endgroup$
    – Abe
    Commented Jul 4, 2011 at 18:26
  • $\begingroup$ Well, that's a big question! One place to find a lot of information about this is Koller and Friedman, Probabilistic Graphical Models. $\endgroup$
    – N F
    Commented Jul 5, 2011 at 2:11

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