Recent content by Stochasticus

It seems I was overthinking this. I was aware that for the whole set of variables, call it big X = {x_{1},...,x_{n}} the sampler met the Markov criterion. I got caught up trying to prove that each subsequent value x_{i}^{t+1} was conditioned only on x_{i}^{t}.

I'm trying to learn more about Markov chains and came across the Gibbs sampler 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...