Computationally Efficient Multivariate Spatio-Temporal Models for High-Dimensional Count-Valued Data (with Discussion)
Computationally Efficient Multivariate Spatio-Temporal Models for High-Dimensional Count-Valued Data (with Discussion)
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DOI：
10.1214/17-ba1069
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发表时间：
2018-03-01
影响因子：
4.4
通讯作者：
Wikle, Christopher K.
中科院分区：
文献类型：
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作者：
Bradley, Jonathan R.;Holan, Scott H.;Wikle, Christopher K.
我们介绍了一个计算效率高的贝叶斯模型预测高维相依计数值数据。在这种情况下，具有潜在高斯过程模型的泊松数据模型已成为事实上的模型。然而，该模型可能难以在高维设置中使用，其中数据可能在不同的变量、地理区域和时间上被制成表格。这些计算困难进一步加剧了承认计数值数据自然是非高斯的。因此，许多目前的方法，在贝叶斯推理，需要仔细校准马尔可夫链蒙特卡罗（MCMC）技术。我们避免MCMC方法，需要调整开发一个新的共轭多元分布。具体来说，我们引入了一个多元对数伽玛分布，并提供了大量的方法发展的独立利益，包括：结果条件分布，边际分布，与多元正态分布的渐近关系，并充分条件分布的吉布斯采样器。为了将变量，区域和时间点之间的依赖关系，使用多变量时空混合效应模型（MSTM）。为了证明我们的方法，我们使用的数据来自美国人口普查局的纵向雇主-家庭动态（LEHD）计划。特别是，我们的方法是由LEHD的季度劳动力指标（QWI），这构成了目前的重要美国经济变量的估计动机。
We introduce a computationally efficient Bayesian model for predicting high-dimensional dependent count-valued data. In this setting, the Poisson data model with a latent Gaussian process model has become the de facto model. However, this model can be difficult to use in high dimensional settings, where the data may be tabulated over different variables, geographic regions, and times. These computational difficulties are further exacerbated by acknowledging that count-valued data are naturally non-Gaussian. Thus, many of the current approaches, in Bayesian inference, require one to carefully calibrate a Markov chain Monte Carlo (MCMC) technique. We avoid MCMC methods that require tuning by developing a new conjugate multivariate distribution. Specifically, we introduce a multivariate log-gamma distribution and provide substantial methodological development of independent interest including: results regarding conditional distributions, marginal distributions, an asymptotic relationship with the multivariate normal distribution, and full-conditional distributions for a Gibbs sampler. To incorporate dependence between variables, regions, and time points, a multivariate spatio-temporal mixed effects model (MSTM) is used. To demonstrate our methodology we use data obtained from the US Census Bureau's Longitudinal Employer-Household Dynamics (LEHD) program. In particular, our approach is motivated by the LEHD's Quarterly Workforce Indicators (QWIs), which constitute current estimates of important US economic variables.