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:模拟模型往往缺乏可移动的可能性功能,这使得无概率推断方法不可或缺。 近贝耶斯计算通过某种距离测量比较模拟和观测数据,产生无概率的后子体样本,但现有方法往往不适于时间序列模拟器,例如由于独立和分布相同的数据假设。在本文件中,我们提议使用近似巴耶斯计算中的路径签名来处理时间序列的顺序性质。我们为由此产生的后子体提供理论保证,并展示产生单体序列、多变式序列、不定期空间序列甚至非单子序列的模拟器具有竞争性的巴耶斯参数推论。