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首页> 外文期刊>Journal of Computational Physics >Gaussian process enhanced semi-automatic approximate Bayesian computation: parameter inference in a stochastic differential equation system for chemotaxis
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Gaussian process enhanced semi-automatic approximate Bayesian computation: parameter inference in a stochastic differential equation system for chemotaxis

机译：高斯工艺增强了半自动近似贝叶斯计算：Chemotaxis的随机微分方程系统中的参数推断

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摘要

Chemotaxis is a type of cell movement in response to a chemical stimulus which plays a key role in multiple biophysical processes, such as embryogenesis and wound healing, and which is crucial for understanding metastasis in cancer research. In the literature, chemotaxis has been modelled using biophysical models based on systems of nonlinear stochastic partial differential equations (NSPDEs), which are known to be challenging for statistical inference due to the intractability of the associated likelihood and the high computational costs of their numerical integration. Therefore, data analysis in this context has been limited to comparing predictions from NSPDE models to laboratory data using simple descriptive statistics. We present a statistically rigorous framework for parameter estimation in complex biophysical systems described by NSPDEs such as the one of chemotaxis. We adopt a likelihood-free approach based on approximate Bayesian computations with sequential Monte Carlo (ABC-SMC) which allows for circumventing the intractability of the likelihood. To find informative summary statistics, crucial for the performance of ABC, we propose to use a Gaussian process (GP) regression model. The interpolation provided by the GP regression turns out useful on its own merits: it relatively accurately estimates the parameters of the NSPDE model and allows for uncertainty quantification, at a very low computational cost. Our proposed methodology allows for a considerable part of computations to be completed before having observed any data, providing a practical toolbox to experimental scientists whose modes of operation frequently involve experiments and inference taking place at distinct points in time. In an application to externally provided synthetic data we demonstrate that the correction provided by ABC-SMC is essential for accurate estimation of some of the NSPDE model parameters and for more flexible uncertainty quantification. (C) 2020 Elsevier Inc. All rights reserved.
机译：趋化性是一种细胞对化学刺激的反应，在胚胎发生和伤口愈合等多种生物物理过程中起关键作用，对理解癌症研究中的转移至关重要。在文献中，趋化性是使用基于非线性随机偏微分方程（NSPDE）系统的生物物理模型建模的，众所周知，由于相关可能性的难解性和数值积分的高计算成本，这些模型对统计推断具有挑战性。因此，这种情况下的数据分析仅限于使用简单的描述性统计将NSPDE模型的预测与实验室数据进行比较。我们提出了一个严格的统计框架，用于NSPDEs描述的复杂生物物理系统的参数估计，例如趋化性系统。我们采用了一种基于序贯蒙特卡罗近似贝叶斯计算（ABC-SMC）的无似然方法，该方法允许规避似然的难解性。为了找到对ABC性能至关重要的信息性汇总统计数据，我们建议使用高斯过程（GP）回归模型。GP回归所提供的插值本身就很有用：它相对准确地估计了NSPDE模型的参数，并允许以非常低的计算成本进行不确定性量化。我们提出的方法允许在观察任何数据之前完成相当一部分计算，为实验科学家提供了一个实用的工具箱，他们的操作模式经常涉及在不同时间点进行的实验和推理。在对外部提供的合成数据的应用中，我们证明了ABC-SMC提供的校正对于准确估计某些NSPDE模型参数和更灵活的不确定性量化至关重要。（C） 2020爱思唯尔公司版权所有。

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