On modeling discrete lattice data using the Potts model

Music City Center 

The analysis of spatial data on a grid is a widely used tool in fields like demography, epidemiology, image analysis, and land management. The Ising and Potts models are often used for such data, for instance in studying protein structures in biology, reconstruction of social networks in social sciences, and image segmentation in computer vision. However, in high-correlation settings simulations from the fitted models are not able to reproduce the characteristics observed in the data. Furthermore, likelihood-based inference is challenging due to an intractable normalizing constant that is a function of the model parameters. We propose a novel tapered version of the Potts models that builds on work from Fellows and Handcock in the context of exponential family random graph models. We show that the tapered model is a valuable alternative to the Potts model and provide an algorithm to fit the model. Based on real and simulated data studies, we provide practical guidance on when to use the tapered model, along with a discussion of its potential limitations.

Potts model

Lattice data modeling

Discrete lattice data 

Section on Statistics and the Environment