Bayesian inference typically relies on a large number of model evaluations to estimate posterior distributions. Established methods like Markov Chain Monte Carlo (MCMC) and Amortized Bayesian Inference (ABI) can become computationally challenging. While ABI enables fast inference after training, generating sufficient training data still requires thousands of model simulations, which is infeasible for expensive models. Surrogate models offer a solution by providing approximate simulations at a lower computational cost, allowing the generation of large data sets for training. However, the introduced approximation errors and uncertainties can lead to overconfident posterior estimates. To address this, we propose Uncertainty-Aware Surrogate-based Amortized Bayesian Inference (UA-SABI) -- a framework that combines surrogate modeling and ABI while explicitly quantifying and propagating surrogate uncertainties through the inference pipeline. Our experiments show that this approach enables reliable, fast, and repeated Bayesian inference for computationally expensive models, even under tight time constraints.

翻译：贝叶斯推理通常依赖于大量模型评估来估计后验分布。传统方法如马尔可夫链蒙特卡洛（MCMC）和摊销贝叶斯推理（ABI）在计算上可能变得极具挑战性。尽管ABI在训练后能够实现快速推理，但生成足够的训练数据仍需要数千次模型模拟，这对于计算昂贵的模型而言是不可行的。代理模型通过以较低计算成本提供近似模拟，为解决此问题提供了方案，从而能够生成用于训练的大规模数据集。然而，引入的近似误差和不确定性可能导致后验估计过度自信。为解决这一问题，我们提出了不确定性感知的基于代理模型的摊销贝叶斯推理（UA-SABI）——一个将代理建模与ABI相结合，同时在推理流程中明确量化和传播代理不确定性的框架。我们的实验表明，即使在严格的时间限制下，该方法也能为计算昂贵的模型实现可靠、快速且可重复的贝叶斯推理。