两阶段MCMC用于大规模时空数据快速贝叶斯推断的三个案例研究
Three Case Studies of Two-stage MCMC for Fast Bayesian Inference of Large Spatio-temporal Data
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中文总结 AI 辅助
本文通过三个案例展示两阶段MCMC算法，以较低计算成本高效拟合大规模贝叶斯时空模型，在保持后验样本一致的同时，实现约一个数量级的计算效率提升。
中文摘要 AI 辅助
高维时空模型往往会迅速遇到计算限制。递归或多阶段贝叶斯算法是应对这一计算挑战的一种方式。在此，我们考虑一种日益常用的两阶段算法。第一阶段在空间上独立且并行地对各个位置进行建模。利用Metropolis-within-Gibbs方法以及适当计算的接受比率，从该第一阶段模型中重采样粒子，可以以较低的计算成本在位置之间施加空间依赖性，同时以总计算成本的一小部分，针对与单阶段MCMC算法相同的后验分布。在本文中，我们展示了三个完整示例，说明如何使用两阶段MCMC算法高效地将贝叶斯时空模型拟合到大型数据集。具体而言，我们考虑：一个利用固有条件自回归（ICAR）先验分布的面积数据上的时空自激发计数模型；一个使用平稳、各向同性的基于距离的协方差函数的点参考数据时空模型；以及一个拟合到空间格点数据上的二元模型，利用潜在高斯过程捕获所有时空依赖性。在每个示例中，我们定义模型并描述相应的两阶段MCMC方法。然后，我们将所得的后验样本和计算效率与使用标准单阶段MCMC算法获得的结果进行比较。尽管在三个示例和众多参数中有所变化，两阶段方法通常可实现约一个数量级的更高计算效率，且两阶段和单阶段算法产生的后验样本高度一致。
英文摘要
High dimensional spatio-temporal models can quickly run up against computational limitations. Recursive or multi-stage Bayesian algorithms are one way to address this computational challenge. Here we consider an increasingly used two-stage algorithm. The first stage models locations independently and in parallel across space. Resampling particles from this stage-one model with Metropolis-within-Gibbs methods and suitably computed acceptance ratios can impose spatial dependence across locations at a low computational cost, while targeting the same posterior distribution as the single-stage MCMC algorithm at a fraction of the overall computational cost. In this paper we show three complete examples of how two-stage MCMC algorithms can be used to efficiently fit Bayesian spatio-temporal models to large datasets. Specifically, we consider: a spatio-temporal self-exciting count model on areal data utilizing intrinsic conditional autoregressive (ICAR) prior distributions; a spatio-temporal model of point-referenced data using a stationary, isotropic distance-based covariance function; and a binary model fit to data on a spatial lattice utilizing a latent Gaussian process to capture all spatio-temporal dependence. In each example, we define the model and describe the corresponding two-stage MCMC approach. We then compare the resulting posterior samples and computational efficiency with those obtained using a standard single-stage MCMC algorithm. While varying across the three examples and numerous parameters, the two-stage approach often achieves roughly an order of magnitude higher computational efficiency, with the two-stage and single-stage algorithms producing closely agreeing posterior samples.
发表机构
- Department of Statistical Sciences, Wake Forest University（维克森林大学统计科学系）
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