Gibbs sampling

1. initial value $X^{(0)}$
2. update $j$th component by $p(x_j | x_1^{(i+1)}, \cdots , x_{j-1}^{(i+1)}, x_{j+1}^{(i)}, \cdots , x_n^{(i)})$
3. repeat

(from wikipedia)


cf. block gibbs sampling
update  $j$th component by $p(x_j | x_1^{(i)}, \cdots , x_{j-1}^{(i)}, x_{j+1}^{(i)}, \cdots , x_n^{(i)})$