he objective is to approximate the posterior distribution $\pi(\phi,\xi|\mathcal D)$ where $\phi$ are the kernel parameters and $\xi=((w_{ik})_{i=0,\ldots,V,k=0,\ldots,p},(a_k,b_k)_{k=0,\ldots,p},\alpha,\sigma,\tau)$, the parameters and hyperparameters of the compound CRM. 