{
  "abstract": "Large spatial data sets now record many correlated variables at many thousands of locations, often on domains where Euclidean distance misrepresents proximity. The central difficulty is modelling the cross-variable dependence jointly while retaining variable-level interpretation. We introduce the bigraphical Mat'ern-Whittle process, a multivariate Gaussian process that resolves this with two graphs. A spatial graph generates the Mat'ern structure of each variable through a fractional power of a graph Laplacian, so the process is valid on any topology, with per-variable range, smoothness and amplitude. A directed acyclic variable graph encodes the scientific structure: we prove that each absent edge yields an exact conditional independence between the corresponding fields. We further prove that the operator determinant does not involve the cross-dependence coefficients, which keeps matrix-free likelihood evaluation and Bayesian learning of the variable graph tractable at scale. Estimation requires only sparse matrix-vector products and scales to tens of millions of space-variable pairs. In simulations the method recovered parameters and graphs accurately, remained robust under misspecification, and halved held-out prediction error on a non-convex domain. In a spatial transcriptomics section with 19,809 cells and 1,122 genes, fitted in 75 minutes on a laptop, borrowing across the learned gene graph reduced held-out prediction error by 50 to 91 percent. Theoretical challenges, such as the achievable efficiency of estimating the variance of the nugget, are also explored.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01950",
  "author_total": 3,
  "authors": [
    {
      "name": "Debangan Dey"
    },
    {
      "name": "Alokesh Manna"
    },
    {
      "name": "Christopher J. Geoga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c00p77y93bva2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01950",
  "fulltext_url": null,
  "id": "c00p77y93bva2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01950",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7207677596",
  "pdf_url": "https://arxiv.org/pdf/2609.01950",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c00p77y93bva2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:42Z",
      "native_id": "2609.01950",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01950"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Bigraphical Matérn-Whittle (BMW) Processes for Fast Inference of Big Multivariate Spatial Data on General Domains",
  "title_text": "Bigraphical Matérn-Whittle (BMW) Processes for Fast Inference of Big Multivariate Spatial Data on General Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:42Z",
  "url": "https://research.draconitic.com/paper/c00p77y93bva2",
  "venue": "arXiv",
  "versions": []
}