I'm trying to learn more about Markov chains and came across the Gibbs sampler(adsbygoogle = window.adsbygoogle || []).push({});

x_1{t+1} ~ p(x_1|x_2 = x_2{t},...x_n{t})

x_2{t+1} ~ p(x_2|x_1 = x_1{t+1},x_3 = x_3{t},...,x_n{t})

.

.

.

x_i{t+1} ~ p(x_i|x_1 = x_1{t+1},...,x_(i-1) = x_(i-1){t+1},x_(i+1) = x_(i+1){t},...,x_n{t})

Supposedly this thing is a Markov chain. I just don't see it. It sure looks like each updated variable x_i{t+1} is contingent on the whole set, not just the prior value x_i{t}. Can someone show me how this satisfies the Markov criterion

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# Gibbs sampler as a Markov process

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