What is Gibbs sampling?

hard

Answer

$p({\theta}_{j}\; \mid \;{\theta}_{- j}, \;D)$
$Guaranteed acceptance (α = 1) when full conditionals are known.$
$Works well for conjugate hierarchical models, Bayesian networks, LDA.$
$Weak in strongly correlated posteriors — slow mixing.$
$Modern alternatives (HMC, NUTS) are usually better default, but Gibbs is still standard when conjugacy makes full conditionals trivial.$

Check yourself — multiple choice

Same as HMC
Sample each parameter from its full conditional $p({\theta}_{j}\; \mid \;{\theta}_{- j}, \;D)$ ; no rejection; great for conjugate / LDA / Bayes nets; slow in correlated posteriors
Random
Not MCMC

Gibbs: draw from full conditionals; α=1; slow when correlated.

#bayesian#mcmc

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