论文标题
贝叶斯模型比较中的元不确定性
Meta-Uncertainty in Bayesian Model Comparison
论文作者
论文摘要
贝叶斯模型比较（BMC）提供了一种原则性的概率方法来研究和对竞争模型进行排名。在标准BMC中，我们在可能的模型集上构建了一个离散的概率分布，以观察到的目标数据为条件。这些后模型概率（PMP）是不确定性的度量，但是当从有限数量的观测值中得出时，也是不确定的。在本文中，我们概念化了BMC中出现的不同级别的不确定性级别。我们探索了一个完全概率的框架，用于量化元不确定性，从而实现了一种增强BMC工作流程的应用方法。利用贝叶斯和频繁的技术，我们通过元模型代表了不确定PMP的不确定性，将模拟和观察到的数据结合到PMP的新数据中的PMP的预测分布中。我们在共轭贝叶斯回归，基于Markov Chain Monte Carlo的可能性推理以及基于神经网络的基于模拟的推理的背景下证明了所提出的方法的实用性。
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed data of interest. These posterior model probabilities (PMPs) are measures of uncertainty, but -- when derived from a finite number of observations -- are also uncertain themselves. In this paper, we conceptualize distinct levels of uncertainty which arise in BMC. We explore a fully probabilistic framework for quantifying meta-uncertainty, resulting in an applied method to enhance any BMC workflow. Drawing on both Bayesian and frequentist techniques, we represent the uncertainty over the uncertain PMPs via meta-models which combine simulated and observed data into a predictive distribution for PMPs on new data. We demonstrate the utility of the proposed method in the context of conjugate Bayesian regression, likelihood-based inference with Markov chain Monte Carlo, and simulation-based inference with neural networks.
