Bayesian Nonparametric Approaches to Ordinal Drought Modeling in the United States

2026-09-22

AI Summary

本文使用贝叶斯非参数方法增强高斯潜变量模型的灵活性，以解决美国序数干旱数据建模中的计算复杂性和模型限制问题。

Abstract

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.

Problem

• Bayesian nonparametric
• ordinal data
• drought modeling
• computational cost
• spatial and temporal dependence

Innovation

• Bayesian nonparametric
• Dirichlet process priors
• Gaussian latent model
• ordinal drought data
• temporal dependence