Joint spatial dependence and Bayesian nonparametric modeling

Develop a model that captures spatial dependence alongside Bayesian nonparametric priors for ordinal drought data, and characterize the resulting increase in model complexity.

Background

The presented models are fitted separately at each spatial location and incorporate temporal dependence through Fourier basis functions, but they do not model dependence across locations. The discussion identifies the simultaneous treatment of spatial dependence and Bayesian nonparametric priors as an unresolved extension.

The problem is motivated by the need to extend the framework from location-specific modeling to a genuinely spatio-temporal Bayesian nonparametric model while understanding the computational and structural consequences.

References

Another open question is how spatial dependence could be captured alongside the use of BNP priors, and how the resulting model complexity would lead to a growth in computational complexity.

— Bayesian Nonparametric Approaches to Ordinal Drought Modeling in the United States  (2609.27135 - Shams et al., 22 Sep 2026) in Section 5, Discussion