Scalable Bayesian inference for high-dimensional mixed-type multivariate spatial data

2025-10-15

AI Summary

Joint modeling of high-dimensional, multivariate spatial response data—comprising binary, count, and continuous types—is challenging; conventional multivariate Gaussian processes (MGPs) become computationally infeasible for large spatial datasets. Method: We propose a Bayesian inference framework based on latent-variable MGPs, accommodating arbitrary exponential-family responses. It employs the Vecchia approximation to achieve linear computational complexity in the number of spatial locations and integrates elliptical slice sampling with a block Metropolis-within-Gibbs algorithm for efficient, stable posterior inference. The model enforces strict identifiability and ensures valid covariance structure specification. Contribution/Results: In simulation studies and a real-world application jointly modeling U.S. wildfire counts and burned area, our approach achieves substantial gains in both computational efficiency and predictive accuracy. It demonstrates strong scalability and practical utility for complex, mixed-type spatial data.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Spatial generalized linear mixed-effects methods are popularly used to model spatially indexed univariate responses. However, with modern technology, it is common to observe vector-valued mixed-type responses, e.g., a combination of binary, count, or continuous types, at each location. Methods that allow joint modeling of such mixed-type multivariate spatial responses are rare. Using latent multivariate Gaussian processes (GPs), we present a class of Bayesian spatial methods that can be employed for any combination of exponential family responses. Since multivariate GP-based methods can suffer from computational bottlenecks when the number of spatial locations is high, we further employ a computationally efficient Vecchia approximation for fast posterior inference and prediction. Key theoretical properties of the proposed model, such as identifiability and the structure of the induced covariance, are established. Our approach employs a Markov chain Monte Carlo-based inference method that utilizes elliptical slice sampling in a blocked Metropolis-within-Gibbs sampling framework. We illustrate the efficacy of the proposed method through simulation studies and a real-data application on joint modeling of wildfire counts and burnt areas across the United States.

Problem

• Modeling multivariate spatial data with mixed response types
• Addressing computational bottlenecks in high-dimensional Bayesian inference
• Enabling joint analysis of spatially correlated mixed-type outcomes

Innovation

• Latent multivariate Gaussian processes for mixed-type responses
• Vecchia approximation for scalable spatial computation
• Elliptical slice sampling in Gibbs framework