Rapid Bayesian Inference for Expensive Stochastic Models

Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the simulation of models are growing even faster. This is largely due to the increase in model complexity, often including stochastic dynamics, that is necessary to describe and characterize phenomena observed using modern, high resolution, experimental techniques. Such models are rarely analytically tractable, meaning that extremely large numbers of stochastic simulations are required for parameter inference. In such cases, parameter inference can be practically impossible. In this work, we present new computational Bayesian techniques that accelerate inference for expensive stochastic models by using computationally inexpensive approximations to inform feasible regions in parameter space, and through learning transforms that adjust the biased approximate inferences to closer represent the correct inferences under the expensive stochastic model. Using topical examples from ecology and cell biology, we demonstrate a speed improvement of an order of magnitude without any loss in accuracy. This represents a substantial improvement over current state-of-the-art methods for Bayesian computations when appropriate model approximations are available. Supplementary files for this article are available online.

几乎所有科学领域均依赖统计推断，以估算理论与计算模型中的未知参数。尽管现代计算机硬件性能持续提升，但模型仿真的计算需求增长速度反而更快。这主要源于模型复杂度的提升——为描述和表征采用现代高分辨率实验技术观测到的自然现象，模型往往需要纳入随机动力学等复杂要素。此类模型极少具备解析可解性，因此参数推断需要开展海量随机仿真实验，在此类场景下，参数推断几乎无法实现。本研究提出了新型计算贝叶斯（computational Bayesian）技术：通过采用计算成本较低的近似方法划定参数空间中的可行区域，并通过学习变换校正有偏的近似推断结果，使其更贴近高成本随机模型下的真实推断结果，从而加速高成本随机模型的参数推断过程。本研究以生态学与细胞生物学中的典型案例为验证对象，证明该方法可将推断速度提升一个数量级，且不会损失任何推断精度。在可获取合适模型近似方法的场景下，该方法相较贝叶斯计算领域当前的最先进方法，实现了性能的大幅提升。本文的补充材料可在线获取。