Algorithm 1: Two-dimensional Gibbs sampling

1 Initialization $X_0=x_0 Y_0=y_0$

2 At t = 0,1,..., loop sampling

2.1 $y_{t+1}\sim p\left(y\mid x_t\right)$

2.2 $x_{t+1}\sim p\left(x\mid y_{t+1}\right)$