We present an algorithmic solution to the problem of incremental belief updating in the context of Monte Carlo inference in Bayesian statistical models represented by probabilistic programs. Given a model and a sample-approximated posterior, our solution constructs a set of weighted observations to condition the model such that inference would result in the same posterior. This problem arises e.g. in multi-level modelling, incremental inference, inference in presence of privacy constraints. First, a set of virtual observations is selected, then, observation weights are found through a computationally efficient optimization procedure such that the reconstructed posterior coincides with or closely approximates the original posterior. We implement and apply the solution to a number of didactic examples and case studies, showing efficiency and robustness of our approach. The provided reference implementation is agnostic to the probabilistic programming language or the inference algorithm, and can be applied to most mainstream probabilistic programming environments.

翻译：本文提出了一种在概率程序表示的贝叶斯统计模型中，针对蒙特卡洛推理进行增量信念更新的算法解决方案。给定一个模型和样本近似的后验分布，我们的方法构建一组加权观测值来约束模型，使得推理结果得到相同的后验分布。该问题出现在例如多层次建模、增量推理、隐私约束下的推理等场景中。首先，选择一组虚拟观测值；然后，通过计算高效的优化过程确定观测权重，使得重建的后验分布与原始后验分布一致或高度近似。我们在一系列教学示例和案例研究中实施并应用了该方案，展示了方法的效率和鲁棒性。所提供的参考实现与概率编程语言或推理算法无关，可适用于大多数主流概率编程环境。