美国有序干旱建模的贝叶斯非参数方法
Bayesian Nonparametric Approaches to Ordinal Drought Modeling in the United States
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中文总结 AI 辅助
本文提出贝叶斯非参数方法增强高斯潜在模型，用于美国时空有序干旱数据建模，通过狄利克雷过程先验捕获时间聚类，以合理计算成本优于参数方法。
中文摘要 AI 辅助
在空间和时间上观测到的数据可能在两个维度上都表现出依赖性，并且数据集在位置数量和时间段数量上可能变得非常庞大。这种依赖性和数据规模意味着，由于密集矩阵求逆、大参数空间或内存和存储挑战，许多统计模型无法以合理的计算成本进行拟合。当数据是有序的时，这只会增加模型拟合的计算复杂性。许多有序模型依赖于一个潜在连续变量，该变量旨在以计算高效的方式捕获依赖性，然后根据截止参数进行划分以产生观测到的有序响应数据。一个非常常见的选择是潜在高斯分布，它可以适应不同的依赖结构，并允许在贝叶斯框架中进行吉布斯采样。不幸的是，该模型可能过于严格，无法提供捕获一系列有序结果所需的灵活性。在本文中，我们展示了使用贝叶斯非参数（BNP）方法来增强高斯潜在模型对在空间和时间上观测到的有序干旱数据的模型灵活性，其中狄利克雷过程先验在每个空间位置内的时间段之间引发聚类。在这项工作中，我们在考虑时间依赖性的同时，分别对每个空间位置的有序干旱数据进行建模，但我们不对跨位置的空間依赖性进行建模。我们表明，这些BNP模型通常以合理的计算成本优于贝叶斯参数方法。
英文摘要
Data observed over space and time can exhibit dependence across both dimensions, and datasets can grow very large in both the number of locations and the number of time periods. This dependence and data size mean that many statistical models cannot be fit at a reasonable computational cost as a result of dense matrix inversions, large parameter spaces, or memory and storage challenges. When the data are ordinal, this only adds to the computational complexity of model fitting. Many ordinal models rely on a latent continuous variable designed to capture dependence in a computationally efficient manner, and then partitioned according to cutoff parameters to yield the observed ordinal response data. A very common choice is a latent Gaussian distribution, which can accommodate different dependence structures and permits Gibbs sampling in a Bayesian framework. Unfortunately, this model can be overly restrictive and fails to provide the flexibility needed to capture a range of ordinal outcomes. In this paper, we demonstrate the use of Bayesian nonparametric (BNP) methods to enhance the model flexibility of a Gaussian latent model for ordinal drought data observed over space and time, with Dirichlet process priors inducing clustering among time periods within each spatial location. In this work, we model ordinal drought data separately at each spatial location while accounting for temporal dependence, but we do not model spatial dependence across locations. We show that these BNP models often outperform Bayesian parametric approaches at a reasonable computational cost.
发表机构
- Wake Forest University（维克森林大学）
机构由 AI 辅助整理，请以论文原文为准。
