The Theoretical and Statistical Ising Model: A Practical Guide in R

Abstract

The “Ising model” refers to both the statistical and the theoretical use of the same equation. In this article, we introduce both uses and contrast their differences. We accompany the conceptual introduction with a survey of Ising-related software packages in R. Since the model’s different uses are best understood through simulations, we make this process easily accessible with fully reproducible examples. Using simulations, we show how the theoretical Ising model captures local-alignment dynamics. Subsequently, we present it statistically as a likelihood function for estimating empirical network models from binary data. In this process, we give recommendations on when to use traditional frequentist estimators as well as novel Bayesian options.