Algorithm 2 Gibbs sampling

1: for $k=1:T$ do 2: for $n=1:N\left(k\right)$ do 3:  ${\mathrm{x}}_{k,n}\sim {\pi }_n\left(·\left|{\mathrm{x}}_{k,1:n-1},{\mathrm{x}}_{k-1,n+1:N\left(k\right)}\right.\right)$; 4: end for 5: $X_k=\left\{{\mathrm{x}}_{k,1},\cdots ,{\mathrm{x}}_{k,N\left(k\right)}\right\}$; 6: end for