Approximate Bayesian computation with the Wasserstein distance
Approximate Bayesian computation with the Wasserstein distance
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DOI：
10.1111/rssb.12312
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发表时间：
2019-04-01
影响因子：
5.8
通讯作者：
Robert, Christian P.
中科院分区：
文献类型：
--
作者：
Bernton, Espen;Jacob, Pierre E.;Robert, Christian P.
越来越多的生成式统计模型不允许其似然函数的数值评估。近似贝叶斯计算已经成为一种流行的方法来克服这个问题，其中一个模拟给定参数的合成数据集，并比较这些数据集的摘要与相应的观测值。我们建议，以避免使用的摘要和随之而来的信息丢失，而是使用观察到的和合成数据的经验分布之间的Wasserstein距离。这将在近似贝叶斯计算中使用顺序统计量的众所周知的方法推广到任意维度。我们描述了最近开发的近似的Wasserstein距离允许的方法来缩放到现实的数据大小，我们提出了一个新的距离的基础上的希尔伯特空间填充曲线。我们提供了一个理论研究所提出的方法，描述一致性的阈值为0，而观察保持固定，和浓度属性的观察数量的增长。各种扩展的时间序列数据进行了讨论。该方法说明了各种例子，包括单变量和多变量的g和k分布，切换开关模型从系统生物学，排队模型和利维驱动的随机波动模型。
A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values. We propose to avoid the use of summaries and the ensuing loss of information by instead using the Wasserstein distance between the empirical distributions of the observed and synthetic data. This generalizes the well-known approach of using order statistics within approximate Bayesian computation to arbitrary dimensions. We describe how recently developed approximations of the Wasserstein distance allow the method to scale to realistic data sizes, and we propose a new distance based on the Hilbert space filling curve. We provide a theoretical study of the method proposed, describing consistency as the threshold goes to 0 while the observations are kept fixed, and concentration properties as the number of observations grows. Various extensions to time series data are discussed. The approach is illustrated on various examples, including univariate and multivariate g-and-k distributions, a toggle switch model from systems biology, a queuing model and a Levy-driven stochastic volatility model.