Bayesian inference for the automultinomial model with an application to landcover data

2026-02-12

AI Summary

This study addresses the computational challenges in modeling multiclass lattice data arising from intractable normalization constants in the likelihood function. Within a Bayesian framework, it systematically applies the Double-Metropolis Hastings algorithm for the first time to perform parameter inference for the automultinomial model, complemented by posterior convergence diagnostics to ensure inferential reliability. The proposed approach effectively handles multiclass spatially dependent data with covariates, circumventing the computational bottlenecks of conventional likelihood-based methods. Simulation studies and an empirical land cover analysis demonstrate that the model offers both flexibility and parsimony across a wide range of spatial dependence structures, outperforming spatial generalized linear mixed models in large-data settings. The work also provides practical guidance for model implementation and computation in real-world applications.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

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
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Multicategory lattice data arise in a wide variety of disciplines such as image analysis, biology, and forestry. We consider modeling such data with the automultinomial model, which can be viewed as a natural extension of the autologistic model to multicategory responses, or equivalently as an extension of the Potts model that incorporates covariate information into a pure-intercept model. The automultinomial model has the advantage of having a unique parameter that controls the spatial correlation. However, the model's likelihood involves an intractable normalizing function of the model parameters that poses serious computational problems for likelihood-based inference. We address this difficulty by performing Bayesian inference through the Double-Metropolis Hastings algorithm, and implement diagnostics to assess the convergence to the target posterior distribution. Through simulation studies and an application to land cover data, we find that the automultinomial model is flexible across a wide range of spatial correlations while maintaining a relatively simple specification. For large data sets we find it also has advantages over spatial generalized linear mixed models. To make this model practical for scientists, we provide recommendations for its specification and computational implementation.

Problem

• automultinomial model
• intractable normalizing constant
• Bayesian inference
• spatial correlation
• likelihood-based inference

Innovation

• automultinomial model
• Bayesian inference
• Double-Metropolis Hastings algorithm
• intractable normalizing constant
• spatial multinomial data