Bayesian Nonparametric Approaches to Ordinal Drought Modeling in the United States
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.
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BibTeX
@misc{shams2026bayesian,
title = {{Bayesian Nonparametric Approaches to Ordinal Drought Modeling in the United States}},
author = {Mostafa Shams and Robert Erhardt and Staci Hepler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27135},
eprint = {2609.27135},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27135},
}
RIS
TY - UNPB
TI - Bayesian Nonparametric Approaches to Ordinal Drought Modeling in the United States
AU - Mostafa Shams
AU - Robert Erhardt
AU - Staci Hepler
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.27135
UR - https://arxiv.org/abs/2609.27135
AB - 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.
ER -