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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Gibbs sampler as a Markov process

**Physics Forums | Science Articles, Homework Help, Discussion**