Bayesian inference for the automultinomial model

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 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 pose 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 found the automultinomial model to be highly flexible across a wide range of spatial correlation levels while maintaining a relatively simple specification. We also provide practical recommendations for model specification and computational implementation.

Spatial modeling

Multinomial spatial data

Automodels

Asymptotically inexact algorithms

Intractable normalizing functions 

Section on Statistics and the Environment