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Gibbs Sampling
Gibbs Sampling
3 questions
Difficulty 5-6
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Intermediate
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conceptual
Gibbs sampling draws each variable
X
i
from its full conditional
p
(
X
i
∣
X
−
i
)
in turn. When is Gibbs sampling especially appealing compared to Metropolis-Hastings?
Hide and think first
A.
When the joint distribution is hard to evaluate, so any sampler that avoids the joint altogether will perform better
B.
When the full conditionals
p
(
X
i
∣
X
−
i
)
have standard forms that can be sampled directly without rejection
C.
When the joint distribution is unimodal, so Gibbs always mixes faster than Metropolis regardless of parameter geometry
D.
When the posterior has heavy tails, because Gibbs sampling automatically handles tail behavior better than MH
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