🤖 AI Summary
Approximate Bayesian computation (ABC) yields unreliable statistical inference under model misspecification and lacks diagnostic tools for incompatible summary statistics. To address these limitations, we propose the first robust ABC framework designed to withstand model misspecification. Our method introduces a reconstructed distance metric coupled with an uncertainty calibration mechanism, ensuring posterior consistency while enabling robust inference. Additionally, we embed a summary statistic compatibility diagnostic module that identifies and excludes statistics inconsistent with the true data-generating process. Extensive experiments—including both synthetic benchmarks and real-world applications—demonstrate substantial improvements in point estimation accuracy and uncertainty quantification quality over standard ABC and existing robust variants. The proposed framework establishes a new paradigm for trustworthy ABC inference under model misspecification.
📝 Abstract
Approximate Bayesian computation (ABC) is one of the most popular"likelihood-free"methods. These methods have been applied in a wide range of fields by providing solutions to intractable likelihood problems in which exact Bayesian approaches are either infeasible or computationally costly. However, the performance of ABC can be unreliable when dealing with model misspecification. To circumvent the poor behavior of ABC in these settings, we propose a novel ABC approach that is robust to model misspecification. This new method can deliver more accurate statistical inference under model misspecification than alternatives and also enables the detection of summary statistics that are incompatible with the assumed data-generating process. We demonstrate the effectiveness of our approach through several simulated examples, where it delivers more accurate point estimates and uncertainty quantification over standard ABC approaches when the model is misspecified. Additionally, we apply our approach to an empirical example, further showcasing its advantages over alternative methods.