{
  "abstract": "High dimensional spatio-temporal models can quickly run up against computational limitations. Recursive or multi-stage Bayesian algorithms are one way to address this computational challenge. Here we consider an increasingly used two-stage algorithm. The first stage models locations independently and in parallel across space. Resampling particles from this stage-one model with Metropolis-within-Gibbs methods and suitably computed acceptance ratios can impose spatial dependence across locations at a low computational cost, while targeting the same posterior distribution as the single-stage MCMC algorithm at a fraction of the overall computational cost. In this paper we show three complete examples of how two-stage MCMC algorithms can be used to efficiently fit Bayesian spatio-temporal models to large datasets. Specifically, we consider: a spatio-temporal self-exciting count model on areal data utilizing intrinsic conditional autoregressive (ICAR) prior distributions; a spatio-temporal model of point-referenced data using a stationary, isotropic distance-based covariance function; and a binary model fit to data on a spatial lattice utilizing a latent Gaussian process to capture all spatio-temporal dependence. In each example, we define the model and describe the corresponding two-stage MCMC approach. We then compare the resulting posterior samples and computational efficiency with those obtained using a standard single-stage MCMC algorithm. While varying across the three examples and numerous parameters, the two-stage approach often achieves roughly an order of magnitude higher computational efficiency, with the two-stage and single-stage algorithms producing closely agreeing posterior samples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14774",
  "author_total": 3,
  "authors": [
    {
      "name": "Mostafa Shams"
    },
    {
      "name": "Robert Erhardt"
    },
    {
      "name": "Staci Hepler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9s9srv3stf98t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14774",
  "fulltext_url": null,
  "id": "9s9srv3stf98t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14774",
  "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.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7213245469",
  "pdf_url": "https://arxiv.org/pdf/2609.14774",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9s9srv3stf98t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:36Z",
      "native_id": "2609.14774",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14774"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Three Case Studies of Two-stage MCMC for Fast Bayesian Inference of Large Spatio-temporal Data",
  "title_text": "Three Case Studies of Two-stage MCMC for Fast Bayesian Inference of Large Spatio-temporal Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/9s9srv3stf98t",
  "venue": "arXiv",
  "versions": []
}