Model selection in the presence of intractable likelihoods remains a central challenge in Bayesian inference. Approximate Bayesian computation (ABC) provides a flexible likelihood-free framework, but its use for model choice is known to be sensitive to the choice of summary statistics, often leading to poorly calibrated posterior model probabilities. Recent ABC variants based on statistical distances allow comparisons to be performed directly on empirical distributions, avoiding data reduction and offering improved theoretical guarantees under suitable conditions. This paper provides a systematic evaluation of discrepancy-based ABC methods for Bayesian model selection, focusing on their empirical behavior across a range of simulation settings and levels of model complexity. We compare full data ABC approaches based on Wasserstein, Creamer-von-Mises, and maximum mean discrepancy metrics with summary-statistic-based ABC and neural network classifiers. The results highlight settings in which full data ABC yields stable and well-calibrated posterior model probabilities, as well as scenarios where performance degrades due to model overlap or dependence. An application to toad movement models illustrates the practical implications of these findings. Overall, the study clarifies the strengths and limitations of discrepancy-based ABC for likelihood-free model choice and provides guidance for its use in realistic inferential settings.

翻译：在贝叶斯推断中，存在难以处理的似然函数时的模型选择仍然是一个核心挑战。近似贝叶斯计算（ABC）提供了一个灵活的免似然函数框架，但其在模型选择中的应用对摘要统计量的选择较为敏感，往往导致后验模型概率校准不佳。最近基于统计距离的ABC变体允许直接对经验分布进行比较，避免了数据约简，并在适当条件下提供了更好的理论保证。本文系统评估了基于差异度量的ABC方法在贝叶斯模型选择中的表现，重点关注其在不同模拟设置和模型复杂度水平下的经验行为。我们比较了基于Wasserstein距离、Cramér-von-Mises距离和最大均值差异度量的全数据ABC方法与基于摘要统计量的ABC方法及神经网络分类器。研究结果揭示了全数据ABC能够产生稳定且校准良好的后验模型概率的场景，以及因模型重叠或依赖性导致性能下降的情况。对蟾蜍运动模型的应用实例说明了这些发现的实际意义。总体而言，本研究阐明了基于差异度量的ABC方法在免似然函数模型选择中的优势与局限，并为其在实际推断场景中的应用提供了指导。