# Can we always pull a joint posterior apart?

If we have a posterior distribution $$p(A,B|\theta)$$, is it always true that $$p(A,B|\theta) = p(A|\theta)p(B|\theta)?$$

• When everything is conditioned on θ, you can basically ignore it. (Or just pretend θ = "the sky is blue".) Is the statement true in that case? – user541686 Apr 10 at 5:34

No, it is not. In order for that to be true, $$A$$ and $$B$$ should be conditionally independent given $$\theta$$.