A Unified Spatiotemporal Framework for Modeling Censored and Missing Areal Responses

2025-11-21

AI Summary

To address pervasive truncation and missing observations in spatiotemporal regional data, this paper proposes a unified Bayesian spatiotemporal modeling framework. The method innovatively integrates spatial autoregressive (SAR) and directed acyclic graph autoregressive (DAGAR) structures within a Gaussian Markov random field (GMRF) formulation, augmented with a temporal autoregressive (AR) component to enable interpretable joint modeling. Unlike conventional conditional autoregressive (CAR) models, the DAGAR-AR framework flexibly captures asymmetric and heterogeneous spatial dependencies. Its Bayesian inferential paradigm naturally supports uncertainty quantification and simultaneous estimation of missing values. In simulation studies and an empirical application to Beijing CO concentration data, the proposed approach significantly outperforms baseline methods—including limit-of-detection (LOD) substitution and mean imputation—achieving superior predictive accuracy and enhanced structural interpretability.

Technology Category

Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal DataReasoning under Uncertainty: Relational Probabilistic ModelsKnowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSearch and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAGSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We propose a new Bayesian approach for spatiotemporal areal data with censored and missing observations. The method introduces a flexible random effect that combines the spatial dependence structures of the Simultaneous Autoregressive (SAR) and Directed Acyclic Graph Autoregressive (DAGAR) models with a temporal autoregressive component. We demonstrate that this formulation extends both spatial models into a unified spatiotemporal framework, expressing them as Gaussian Markov random fields in their innovation form. The resulting model captures spatial, temporal, and joint spatiotemporal correlations in an interpretable way. Simulation studies show that the proposed model outperforms common ad hoc imputation strategies, such as replacing censored values with the limit of detection (LOD) or imputing missing data by the sample mean. We further apply the method to carbon monoxide (CO) concentration data from Beijing's air quality network, comparing the proposed DAGAR-AR model with the traditional Conditional Autoregressive (CAR) approach. The results indicate that while the CAR model achieves slightly better predictive performance, the DAGAR-AR specification offers clearer interpretability and a more coherent representation of the spatiotemporal dependence structure.

Problem

• Modeling censored and missing spatiotemporal areal data
• Extending spatial models into a unified spatiotemporal framework
• Improving interpretability of spatiotemporal dependence structures

Innovation

• Bayesian approach for censored and missing data
• Combines SAR and DAGAR with temporal autoregressive component
• Unified spatiotemporal framework using Gaussian Markov fields