Distributed Bayesian Inference in Linear Mixed-Effects Models
Distributed Bayesian Inference in Linear Mixed-Effects Models
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DOI：
10.1080/10618600.2020.1869025
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发表时间：
2021-03
影响因子：
2.4
通讯作者：
Sanvesh Srivastava;Yixiang Xu
中科院分区：
文献类型：
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作者：
Sanvesh Srivastava;Yixiang Xu
摘要线性混合效应模型在统计方法学中起着基础性的作用。存在用于拟合这些模型的各种马尔可夫链蒙特卡罗（MCMC）算法，但是它们在大规模数据设置中是低效的，因为任何这样的MCMC算法的每次迭代都通过完整的数据。已经提出了许多分而治之的方法来解决这个问题，但它们缺乏理论保证，强加限制性假设，或者具有复杂的计算算法。我们的重点是一个这样的方法称为Wasserstein后验（WASP），这已成为流行的，由于其最佳的理论性能在一般假设下。不幸的是，WASP的实际实现要么需要解决一个复杂的线性规划，要么仅限于一维参数。前一种方法效率低，后一种方法无法捕捉多元参数的联合后验依赖结构。我们开发了一种新的算法，用于计算的WASP的多变量参数，这是很容易实现的，是有用的计算WASP在任何模型中的后验分布的参数属于一个位置分散家庭的概率措施。该算法介绍了线性混合效应模型的实现细节和理论性质。我们的算法优于目前国家的最先进的方法在推理的随机效应的协方差矩阵的函数在不同的数值比较。本文的补充材料可在网上获得。
Abstract Linear mixed-effects models play a fundamental role in statistical methodology. A variety of Markov chain Monte Carlo (MCMC) algorithms exist for fitting these models, but they are inefficient in massive data settings because every iteration of any such MCMC algorithm passes through the full data. Many divide-and-conquer methods have been proposed to solve this problem, but they lack theoretical guarantees, impose restrictive assumptions, or have complex computational algorithms. Our focus is one such method called the Wasserstein Posterior (WASP), which has become popular due to its optimal theoretical properties under general assumptions. Unfortunately, practical implementation of the WASP either requires solving a complex linear program or is limited to one-dimensional parameters. The former method is inefficient and the latter method fails to capture the joint posterior dependence structure of multivariate parameters. We develop a new algorithm for computing the WASP of multivariate parameters that is easy to implement and is useful for computing the WASP in any model where the posterior distribution of parameter belongs to a location-scatter family of probability measures. The algorithm is introduced for linear mixed-effects models with both implementation details and theoretical properties. Our algorithm outperforms the current state-of-the-art method in inference on the functions of the covariance matrix of the random effects across diverse numerical comparisons. Supplemental materials for this article are available online.