Many scientific models are composed of multiple discrete components, and scien tists often make heuristic decisions about which components to include. Bayesian inference provides a mathematical framework for systematically selecting model components, but defining prior distributions over model components and developing associated inference schemes has been challenging. We approach this problem in an amortized simulation-based inference framework: We define implicit model priors over a fixed set of candidate components and train neural networks to infer joint probability distributions over both, model components and associated parameters from simulations. To represent distributions over model components, we introduce a conditional mixture of multivariate binary distributions in the Grassmann formalism. Our approach can be applied to any compositional stochastic simulator without requiring access to likelihood evaluations. We first illustrate our method on a simple time series model with redundant components and show that it can retrieve joint posterior distribution over a set of symbolic expressions and their parameters while accurately capturing redundancy with strongly correlated posteriors. We then apply our approach to drift-diffusion models, a commonly used model class in cognitive neuroscience. After validating the method on synthetic data, we show that our approach explains experimental data as well as previous methods, but that our fully probabilistic approach can help to discover multiple data-consistent model configurations, as well as reveal non-identifiable model components and parameters. Our method provides a powerful tool for data-driven scientific inquiry which will allow scientists to systematically identify essential model components and make uncertainty-informed modelling decisions.

翻译：许多科学模型由多个离散组件构成，科学家常凭经验判断应纳入哪些组件。贝叶斯推断为系统化选择模型组件提供了数学框架，但定义模型组件上的先验分布并开发相应的推断算法始终具有挑战性。我们采用摊销式仿真推断框架处理这一问题：在固定候选组件集合上定义隐式模型先验，并训练神经网络从仿真数据中推断模型组件及其相关参数的联合概率分布。为表示模型组件上的分布，我们引入格拉斯曼形式体系下的多元二元分布条件混合模型。该方法适用于任意组合式随机模拟器，且无需计算似然函数。我们首先在含冗余组件的简单时间序列模型上验证方法，结果表明其能有效捕获包含符号表达式及其参数的后验联合分布，并通过强相关后验准确反映组件冗余特性。随后将该方法应用于认知神经科学中常用的漂移扩散模型。在合成数据上验证方法有效性后，我们发现本方法对实验数据的解释能力与现有方法相当，但完全概率化方法能帮助发现多个与数据兼容的模型构型，同时揭示无法辨识的模型组件与参数。本方法为数据驱动的科学探索提供了有力工具，使科学家能系统识别核心模型组件，并基于不确定性认知做出建模决策。