We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent variable model, which we refer to as a Gaussian latent machine. This leads to a general sampling approach that unifies and generalizes many existing sampling algorithms in the literature. Most notably, it yields a highly efficient and effective two-block Gibbs sampling approach in the general case, while also specializing to direct sampling algorithms in particular cases. Finally, we present detailed numerical experiments that demonstrate the efficiency and effectiveness of our proposed sampling approach across a wide range of prior and posterior sampling problems from Bayesian imaging.

翻译：我们考虑从一种专家乘积型模型中采样的问题，该模型涵盖贝叶斯成像中常见的多种标准先验和后验分布。我们证明该模型可轻松提升为一种新颖的潜变量模型，称为高斯潜变量机器。这引出了一种通用的采样方法，统一并推广了文献中的许多现有采样算法。最值得注意的是，该方法在一般情况下产生了一种高效且有效的双块吉布斯采样方法，同时在特定情况下可特化为直接采样算法。最后，我们通过详细的数值实验证明，所提出的采样方法在贝叶斯成像中广泛先验与后验采样问题上具有高效性和有效性。