4
$\begingroup$

Been watching this video by Tom Minka on Expectation Propagation (http://videolectures.net/mlss09uk_minka_ai/). At about 19:12, he says that the reason the moment matching technique works is that when you multiply a lot of likelihood terms together, the resulting posterior distribution is compact and its variance is very small and it will look more Gaussian (assuming IID). At some point in the video, he says this is because of the central limit theorem. However, However, I am unable to see how the CLT applies to multiplying such likelihoods and why this should approximate a compact Gaussian.

Would appreciate any thoughts/suggestions on understanding this.

$\endgroup$
4
$\begingroup$

What I meant to say was the Bernstein-von Mises theorem, which is the Bayesian analogue of the central limit theorem.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.