Algorithm 2: Inference with Markov Chain Monte Carlo

input: Training data $\mathcal{D}={\mathit{X}}^{(k)}$, ${\mathit{y}}^{(k)}$, where $k\in 1,\dots ,M$, Hyper-parameters $\mathit{\theta }$;  output: The inference Mean ${\mathit{\mu }}_{*}$ and Variance ${\mathit{\sigma }}_{*}$;