Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and observed data through some distance measure, but existing approaches are often poorly suited to time series simulators, for example due to an independent and identically distributed data assumption. In this paper, we propose to use path signatures in approximate Bayesian computation to handle the sequential nature of time series. We provide theoretical guarantees on the resultant posteriors and demonstrate competitive Bayesian parameter inference for simulators generating univariate, multivariate, irregularly spaced, and even non-Euclidean sequences.

翻译：仿真模型常缺乏易于处理的似然函数，这使得无似然推断方法不可或缺。近似贝叶斯计算通过某种距离度量比较模拟数据与观测数据来生成无似然后验样本，但现有方法往往不适用于时间序列模拟器——例如因其对独立同分布数据的假设。本文提出在近似贝叶斯计算中使用路径特征，以处理时间序列的时序特性。我们为所得后验分布提供了理论保证，并论证了该方法在对生成单变量、多变量、非等间距甚至非欧几里得序列的模拟器进行贝叶斯参数推断中的竞争力。