Bayesian computational algorithms tend to scale poorly as data size increases. This had led to the development of divide-and-conquer-based approaches for scalable inference. These divide the data into subsets, perform inference for each subset in parallel, and then combine these inferences. While appealing theoretical properties and practical performance have been demonstrated for independent observations, scalable inference for dependent data remains challenging. In this work, we study the problem of Bayesian inference from very long time series. The literature in this area focuses mainly on approximate approaches that lack any theoretical guarantees and may provide arbitrarily poor accuracy in practice. We propose a simple and scalable divide-and-conquer method, and provide accuracy guarantees. Numerical simulations and real data applications demonstrate the effectiveness of our approach.
翻译:随着数据规模的增加,贝叶斯计算算法往往规模不高,从而导致制定基于分化和征服的可缩放推论方法。这些方法将数据分为子集,对每个子集进行平行推论,然后将这些推论结合起来。虽然已经为独立观察展示出有吸引力的理论属性和实际性能,但从依赖数据推论的可缩放推论仍然具有挑战性。在这项工作中,我们研究了从很长的时间序列中推断贝叶斯人的问题。这一领域的文献主要侧重于缺乏理论保障、在实践中可能提供任意错误准确性的近似方法。我们提出了一个简单和可缩放的分解和剖法,并提供准确性保证。数字模拟和真实数据应用证明了我们的方法的有效性。