Mathematical Institute, Mathematical Sciences Building, University of Warwick, Coventry, United Kingdom.
Mathematical Institute, Andrew Wiles Building, University of Oxford, Oxford, United Kingdom.
PLoS One. 2020 Aug 6;15(8):e0236954. doi: 10.1371/journal.pone.0236954. eCollection 2020.
To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is that parameter inference must generally rely on summary statistics of the data. This is particularly the case for problems involving high-dimensional data, such as biological imaging experiments. However, some summary statistics contain more information about parameters of interest than others, and it is not always clear how to weight their contributions within the ABC framework. We address this problem by developing an automatic, adaptive algorithm that chooses weights for each summary statistic. Our algorithm aims to maximize the distance between the prior and the approximate posterior by automatically adapting the weights within the ABC distance function. Computationally, we use a nearest neighbour estimator of the distance between distributions. We justify the algorithm theoretically based on properties of the nearest neighbour distance estimator. To demonstrate the effectiveness of our algorithm, we apply it to a variety of test problems, including several stochastic models of biochemical reaction networks, and a spatial model of diffusion, and compare our results with existing algorithms.
为了推断具有棘手似然函数的机械模型的参数，越来越多地采用近似贝叶斯计算 (ABC) 等技术。然而，在实际情况下，ABC 的主要缺点之一是参数推断通常必须依赖于数据的摘要统计信息。对于涉及高维数据的问题（例如生物成像实验）尤其如此。然而，一些摘要统计信息包含有关感兴趣参数的更多信息，并且并不总是清楚如何在 ABC 框架内为它们的贡献加权。我们通过开发一种自动自适应算法来解决此问题，该算法为每个摘要统计信息选择权重。我们的算法旨在通过自动适应 ABC 距离函数中的权重来最大化先验和近似后验之间的距离。在计算上，我们使用分布之间距离的最近邻估计器。我们基于最近邻距离估计器的性质从理论上证明了该算法的有效性。为了证明我们的算法的有效性，我们将其应用于各种测试问题，包括生化反应网络的几个随机模型和扩散的空间模型，并将我们的结果与现有算法进行比较。
