The Hidden Markov Ising Model with Exogenous Covariates

Aari Vinayagasothy; Beamlak Haddis; Oscar Lopez; Ann Manjo; Adam B Kashlak

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arXiv · 2611.05213

The Hidden Markov Ising Model with Exogenous Covariates

Aari Vinayagasothy·Beamlak Haddis·Oscar Lopez·Ann Manjo·Adam B Kashlak

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Abstract

The Ising model, a type of Markov Random Field, from statistical physics has a long history of modeling spatial and network data as well as particle interactions. In this work, we consider inserting the Ising model into the framework of a Hidden Markov Model, a type of Bayesian Network, to model temporal state changes in a sequence of Ising observations. While this is entirely a discrete probability model, a main challenge is the fitting of such a probabilistic graphical model due to the exponential intractability of normalizing constants within the Ising model. To circumvent this problem, we consider the usage of maximum pseudolikelihood estimators that have a long history in Markov Random Fields. Validity of the pseudolikelihood Baum-Welch algorithm, model identifiability under likelihood, and consistency for large networks is also proved. The proposed Hidden Markov Ising Model is further extended to incorporate exogenous variables resulting in a hybrid hidden Markov autologistic model with graphical dependencies integrated into the model. This model is applied to a five year sequence of weekly gun violence events across the 3109 counties of the continental United States to identify state changes in gun violence activity from 2021 to 2025.

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BibTeX RIS

Aari Vinayagasothy, Beamlak Haddis, Oscar Lopez, Ann Manjo, Adam B Kashlak. 2026-11-03. The Hidden Markov Ising Model with Exogenous Covariates. https://arxiv.org/abs/2611.05213

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