Likelihood-free inference (LFI) methods, such as Approximate Bayesian computation (ABC), are now routinely applied to conduct inference in complex models. While the application of LFI is now commonplace, the choice of which summary statistics to use in the construction of the posterior remains an open question that is fraught with both practical and theoretical challenges. Instead of choosing a single vector of summaries on which to base inference, we suggest a new pooled posterior and show how to optimally combine inferences from different LFI posteriors. This pooled approach to inference obviates the need to choose a single vector of summaries, or even a single LFI algorithm, and delivers guaranteed inferential accuracy without requiring the computational resources associated with sampling LFI posteriors in high-dimensions. We illustrate this approach through a series of benchmark examples considered in the LFI literature.
翻译:目前,通常采用无可能性推断法(LFI)方法,如阿普约贝耶斯计算法(ABC),在复杂模型中进行推断。虽然LFI的应用现在司空见惯,但选择用于构建后方的简要统计仍然是个未决问题,既存在实际挑战,也存在理论挑战。我们建议采用新的集合后方数据,并表明如何最佳地将不同LFI后方数据的推断法结合起来。这种合并法推法避免了选择单一摘要矢量,甚至单一LFI算法的必要性,并提供了有保证的推断准确性,而无需与高层中取样LFI后方数据相关的计算资源。我们通过LFI文献中考虑的一系列基准实例来说明这一方法。