Making Recursive Bayesian Inference Accessible
Making Recursive Bayesian Inference Accessible
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DOI：
10.1080/00031305.2019.1665584
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发表时间：
2019-10-16
影响因子：
1.8
通讯作者：
Brost, Brian M.
中科院分区：
文献类型：
--
作者：
Hooten, Mevin B.;Johnson, Devin S.;Brost, Brian M.
贝叶斯模型自然提供递归推理，因为它们可以形式化地协调新数据和现有科学信息。然而，广泛使用的贝叶斯方法通常避免基于先前研究得出的准确的后验分布的先验。现有的两种递归贝叶斯方法是：先验递归贝叶斯和建议递归贝叶斯。先验-递归贝叶斯使用贝叶斯更新，将模型按顺序适配到数据分区，并提供了一种方法，当新数据变得可用时，使用前一阶段的后验作为基于最新数据的新阶段的先验。建议-递归贝叶斯旨在与分层贝叶斯模型一起使用，并在数据分区的第一阶段独立分析中使用一组瞬时先验。建议的第二阶段-递归贝叶斯使用第一阶段的后验作为马尔可夫链蒙特卡罗算法中的建议，以拟合完整的模型。我们结合了先验递归和提议递归的概念，以适应任何贝叶斯模型，并且通常具有计算改进。我们通过两个案例研究来演示我们的方法。我们的方法对大数据、流数据和最佳自适应设计情况都有影响。
Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior distributions resulting from former studies. Two existing Recursive Bayesian methods are: Prior- and Proposal-Recursive Bayes. Prior-Recursive Bayes uses Bayesian updating, fitting models to partitions of data sequentially, and provides a way to accommodate new data as they become available using the posterior from the previous stage as the prior in the new stage based on the latest data. Proposal-Recursive Bayes is intended for use with hierarchical Bayesian models and uses a set of transient priors in first stage independent analyses of the data partitions. The second stage of Proposal-Recursive Bayes uses the posteriors from the first stage as proposals in a Markov chain Monte Carlo algorithm to fit the full model. We combine Prior- and Proposal-Recursive concepts to fit any Bayesian model, and often with computational improvements. We demonstrate our method with two case studies. Our approach has implications for big data, streaming data, and optimal adaptive design situations.