Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular class of hierarchical models due to their high-dimensional nested parameter structure. To address this intractability, we propose a deep learning method for performing BMC on any set of hierarchical models which can be instantiated as probabilistic programs. Since our method enables amortized inference, it allows efficient re-estimation of posterior model probabilities and fast performance validation prior to any real-data application. In a series of extensive validation studies, we benchmark the performance of our method against the state-of-the-art bridge sampling method and demonstrate excellent amortized inference across all BMC settings. We then showcase our method by comparing four hierarchical evidence accumulation models that have previously been deemed intractable for BMC due to partly implicit likelihoods. In this application, we corroborate evidence for the recently proposed L\'evy flight model of decision-making and show how transfer learning can be leveraged to enhance training efficiency. We provide reproducible code for all analyses and an open-source implementation of our method.

翻译：贝叶斯模型比较（BMC）提供了一种评估竞争性计算模型相对优劣、并将不确定性传播到模型选择决策中的原则性方法。然而，由于分层模型具有高维嵌套参数结构，BMC通常难以应用于这类主流模型。为解决这一计算难题，我们提出了一种深度学习框架，可对任何能够实例化为概率程序的分层模型执行BMC。该方法支持摊销推理，使得在实际数据应用前能够高效地重新估计后验模型概率，并快速验证模型性能。通过一系列全面的验证研究，我们将所提方法与当前最先进的桥式采样方法进行基准对比，证明其在所有BMC设置中均表现出优异的摊销推理能力。随后，我们通过比较四种分层证据累积模型来展示该方法——这些模型因部分隐式似然而此前被认为无法进行BMC。在该应用中，我们验证了最近提出的决策者莱维飞行模型的相关证据，并展示了如何利用迁移学习提升训练效率。我们提供了所有分析的可复现代码及本方法的开源实现。