🤖 AI Summary
In likelihood-free inference (LFI), selecting informative summary statistics is challenging when the likelihood is intractable, and individual LFI methods (e.g., ABC, SNPE, BOLFI) often suffer from bias and instability. To address these issues, this paper proposes a provably accurate pooled posterior framework that requires no hand-crafted summary statistics or method-specific assumptions. It integrates posterior estimates from multiple LFI algorithms via weighted Bayesian model averaging and kernel density estimation. Grounded in asymptotically optimal combination theory, the framework avoids high-dimensional posterior sampling while guaranteeing convergence and statistical consistency—thereby substantially improving robustness. Experiments on standard LFI benchmarks demonstrate significant gains in inference accuracy and a tenfold reduction in computational cost compared to state-of-the-art single-method approaches.
📝 Abstract
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.