{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05213",
  "author_total": 5,
  "authors": [
    {
      "name": "Aari Vinayagasothy"
    },
    {
      "name": "Beamlak Haddis"
    },
    {
      "name": "Oscar Lopez"
    },
    {
      "name": "Ann Manjo"
    },
    {
      "name": "Adam B Kashlak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdyrv9amgdfk6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05213",
  "fulltext_url": null,
  "id": "cdyrv9amgdfk6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05213",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.ME"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05213",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdyrv9amgdfk6.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:34Z",
      "native_id": "2611.05213",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05213"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "The Hidden Markov Ising Model with Exogenous Covariates",
  "title_text": "The Hidden Markov Ising Model with Exogenous Covariates",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:10Z",
  "url": "https://research.draconitic.com/paper/cdyrv9amgdfk6",
  "venue": "arXiv",
  "versions": []
}