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）为评估竞争性计算模型的相对优劣及将不确定性传播至模型选择决策提供了原则性方法。然而，对于层级模型这一常见类别，由于其高维嵌套参数结构，BMC通常难以求解。为解决这一难题，我们提出了一种深度学习方法，可对任意可实例化为概率程序的层级模型集合执行BMC。由于该方法支持摊销推断，因此能够在实际数据应用前高效重新估计后验模型概率并快速验证性能。通过一系列广泛验证研究，我们将该方法与最先进的桥接抽样方法进行基准对比，证明其在所有BMC设置下均能实现优异的摊销推断。随后，我们通过比较四个此前因部分似然函数隐含而被认为无法进行BMC的层级证据积累模型来展示该方法。在该应用中，我们证实了近期提出的决策莱维飞行模型的证据，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该方法的开源实现。