Bayesian inference with stochastic models is often difficult because their likelihood functions involve high-dimensional integrals. Approximate Bayesian Computation (ABC) avoids evaluating the likelihood function and instead infers model parameters by comparing model simulations with observations using a few carefully chosen summary statistics and a tolerance that can be decreased over time. Here, we present a new variant of simulated-annealing ABC algorithms, drawing intuition from non-equilibrium thermodynamics. We associate each summary statistic with a state variable (energy) quantifying its distance from the observed value, as well as a temperature that controls the extent to which the statistic contributes to the posterior. We derive an optimal annealing schedule on a Riemannian manifold of state variables based on a minimal-entropy-production principle. We validate our approach on standard benchmark tasks from the simulation-based inference literature as well as on challenging real-world inference problems, and show that it is highly competitive with the state of the art.

翻译：基于随机模型的贝叶斯推断通常因似然函数涉及高维积分而存在困难。近似贝叶斯计算（ABC）通过避免直接计算似然函数，转而利用精心选取的少量摘要统计量及可随时间衰减的容差参数，将模型模拟结果与观测数据进行比较，从而实现模型参数推断。本文提出一种新型模拟退火ABC算法变体，该算法从非平衡态热力学中汲取灵感。我们将每个摘要统计量与表征其与观测值距离的状态变量（能量）相关联，并引入温度参数以控制该统计量对后验分布的贡献程度。基于最小熵产生原理，我们在状态变量的黎曼流形上推导出最优退火调度策略。通过在仿真推断文献中的标准基准任务及具有挑战性的实际推断问题上的验证，我们证明该方法与现有最优技术相比具有高度竞争力。