Simulation-based inference (SBI) has become a widely used framework in applied sciences for estimating the parameters of stochastic models that best explain experimental observations. A central question in this setting is how to effectively combine multiple observations in order to improve parameter inference and obtain sharper posterior distributions. Recent advances in score-based diffusion methods address this problem by constructing a compositional score, obtained by aggregating individual posterior scores within the diffusion process. While it is natural to suspect that the accumulation of individual errors may significantly degrade sampling quality as the number of observations grows, this important theoretical issue has so far remained unexplored. In this paper, we study the compositional score produced by the GAUSS algorithm of Linhart et al. (2024) and establish an upper bound on its mean squared error in terms of both the individual score errors and the number of observations. We illustrate our theoretical findings on a Gaussian example, where all analytical expressions can be derived in a closed form.

翻译：仿真推断（SBI）已成为应用科学中广泛采用的框架，用于估计能最佳解释实验观测的随机模型参数。该框架中的一个核心问题是如何有效整合多个观测数据，以改进参数推断并获得更精确的后验分布。基于评分的扩散方法的最新进展通过构建组合评分来解决这一问题，该评分通过在扩散过程中聚合各个后验评分而获得。尽管人们自然怀疑随着观测数量的增加，个体误差的累积可能会显著降低采样质量，但这一重要的理论问题迄今尚未得到深入探讨。本文研究了 Linhart 等人（2024）提出的 GAUSS 算法生成的组合评分，并基于个体评分误差和观测数量，建立了其均方误差的上界。我们通过一个高斯示例阐释了理论结果，其中所有解析表达式均能以闭合形式导出。