We introduce Sequential Neural Posterior Score Estimation (SNPSE), a score-based method for Bayesian inference in simulator-based models. Our method, inspired by the remarkable success of score-based methods in generative modelling, leverages conditional score-based diffusion models to generate samples from the posterior distribution of interest. The model is trained using an objective function which directly estimates the score of the posterior. We embed the model into a sequential training procedure, which guides simulations using the current approximation of the posterior at the observation of interest, thereby reducing the simulation cost. We also introduce several alternative sequential approaches, and discuss their relative merits. We then validate our method, as well as its amortised, non-sequential, variant on several numerical examples, demonstrating comparable or superior performance to existing state-of-the-art methods such as Sequential Neural Posterior Estimation (SNPE).

翻译：我们提出了序列神经后验分数估计（SNPSE），一种用于基于模拟器模型的贝叶斯推断的分数匹配方法。受分数匹配方法在生成建模中显著成功的启发，我们的方法利用条件分数扩散模型从目标后验分布中生成样本。该模型通过直接估计后验分布分数的目标函数进行训练。我们将模型嵌入序列训练框架，该框架利用当前对目标观测后验的近似来指导模拟，从而降低模拟成本。我们还提出了几种替代的序列化方法，并讨论了它们的相对优势。随后，我们在多个数值算例上验证了本方法及其摊销式非序列变体，结果表明其性能与序列神经后验估计（SNPE）等现有先进方法相当或更优。