{
  "abstract": "Conditional quantiles are central to asymmetric decision losses, tail-risk assessment, and interval forecasts, but Bayesian quantile regression for nonlinear time series can be difficult when the temporal feature vector is high-dimensional. We develop the quantile deep echo state network (Q-DESN), a Bayesian quantile regression model conditional on fixed features generated by a deep echo state network. Conditional on a specified reservoir construction and feature map, posterior uncertainty is assigned to the regression coefficients, likelihood, and shrinkage parameters. Single-level fits use asymmetric Laplace or quantile-fixed generalized asymmetric Laplace working likelihoods with ridge or regularized-horseshoe priors. Posterior computation uses Markov chain Monte Carlo when computationally practical and a model-specific variational Bayes approximation for analyses requiring repeated fitting. For quantile grids, we compare independent level-wise regressions followed by monotone rearrangement with a joint quantile-vector regression that shrinks adjacent quantile-specific coefficient differences. Synthetic studies, a single-origin retrospective Global Flood Awareness System (GloFAS) streamflow case, and a retrospective PriceFM comparison identify settings where this fixed-feature Bayesian regression improves finite-grid quantile scores.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17579",
  "author_total": 3,
  "authors": [
    {
      "name": "Antonio De Leon"
    },
    {
      "name": "Raquel Prado"
    },
    {
      "name": "Bruno Sansó"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/81pqj9grqy09c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17579",
  "fulltext_url": null,
  "id": "81pqj9grqy09c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17579",
  "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.ME"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7213528723",
  "pdf_url": "https://arxiv.org/pdf/2609.17579",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/81pqj9grqy09c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:10Z",
      "native_id": "2609.17579",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17579"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Bayesian Quantile Deep Echo State Networks for Nonlinear Time Series",
  "title_text": "Bayesian Quantile Deep Echo State Networks for Nonlinear Time Series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/81pqj9grqy09c",
  "venue": "arXiv",
  "versions": []
}