homework extension

[Mladen Kolar]

Hi,

due to popular request, assignment 5 is now due Monday, April 5.

Mladen

[Matt Golub]

What is meant by "direct sampling" in 2d? We are given in the hint a factorization of the joint posterior into a product of marginal posteriors. Aren't these the marginal posteriors that we sample from in the Gibbs sampler?

[Aapo Kyrola]

The posterior for mean p(m|s,D) is same as in Gibbs sampling but for
sigma, you need P(s|D) (instead of p(s|m,D) like in Gibbs). Both can
be found by utilizing Bayes rule.

Idea is that you have joint posterior p(m,s|D), you can factorize it
into
p(m,s|D) = p(m|s,D)p(s|D). Then to sample from the joint you first
sample s \sim p(s|D) and then m \sim p(m|s,D) to get sample (m,s).