Question: 14. Consider the generalized Hastings algorithm that uses the following candidate density: q(v, u) = % p(vi|uj=i) for vj=i = uj=i 0 otherwise . That

14. Consider the generalized Hastings algorithm that uses the following candidate density:

q(v, u) = % p(vi|uj=i) for vj=i = uj=i 0 otherwise .

That is, the algorithm chooses (randomly or deterministically) an index i ∈ {1,...,K}, and then uses the full conditional distribution along the i

th coordinate as the candidate density. Show that this algorithm has Hastings acceptance ratio (3.15) identically equal to 1 (as called for by the Gibbs algorithm), and hence that the Gibbs sampler is a special case of the Hastings algorithm.

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