When I checked Wikipedia about Marginal likelihood, I find an equality of the form: $$p(a\mid b)=\int p(a\mid c)\cdot p(c\mid b)\,dc$$ and it's valid because the parameter c is marginalized/integrated out. However, when I tried proving its validity by actually performing integration and sum&product rules of probability, I failed... And I just can't figure out how that marginalization really works.
basically it is not necessarily true unless $p(a|c) = p(a|c,b)$. –  Memming Sep 1 '13 at 18:29