arXiv subjects

Antonio De Leon

Publications and source records attributed to Antonio De Leon.

4 recordsLinked to original sources

arXiv2026

Bayesian Quantile Deep Echo State Networks for Nonlinear Time Series

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.

stat.ME↗

arXiv2026

Mean-Tilted Intervals: Short Tolerance Intervals

Intervals with the same probability content can have different endpoint placements and widths. This matters for tolerance inference, where a reported interval must also satisfy a repeated-sampling content-confidence statement. We develop mean-tilted intervals (MTIs), a fixed-content family indexed by retained-mean balance. The zero-tilt member is the mean-preserving interval (MPI) induced by the residual-product criterion of Pouplin et al.; nonzero tilts move through admissible contiguous windows, including distribution-specific central and shortest intervals. For tolerance inference, we introduce TCSP, a tolerance-calibrated shortest-path action. TCSP chooses the retained order-statistic count by distribution-free scan calibration and reports the shortest closed window at that count. This keeps the certified interval action separate from generalized-posterior endpoint summaries. We also study a calibrated MTI-ECM comparator that profiles fitted content and tilt over a prespecified grid and applies an independent Dirichlet-process content-probability check. In iid simulations at tolerance confidence 0.95, we compare TCSP, MTI-ECM, Young-Mathew interpolation, and Wilks intervals across feasible content-sample-size cells and eight continuous distributions. The study emphasizes skewed distributions, where placement matters most, and excludes cells where the sample range cannot support the requested two-sided distribution-free statement.

stat.ME↗

arXiv2026

Bayesian Quantile-Based Correction and Synthesis of Hydrologic Products

River-flow forecasting requires predictive distributions that remain informative in both routine and extreme conditions. We develop a Bayesian quantile-based correction-and-synthesis framework built on Dynamic Quantile Linear Models (DQLMs). The framework links U.S. Geological Survey (USGS) observations, retrospective products, and ensemble forecast products through a shared latent quantile process, learns dynamic discrepancies for each external source, and combines quantile-specific posterior predictions into a single predictive distribution. We also adapt variational Bayes inference to the extended dynamic quantile linear model using Laplace--Delta approximations for non-conjugate parameters. The methodology is illustrated using daily flow for the San Lorenzo River together with products from the European Centre for Medium-Range Weather Forecasts (ECMWF) Global Flood Awareness System (GloFAS) and the National Oceanic and Atmospheric Administration (NOAA) National Weather Service (NWS), with emphasis on medium-range forecasting and uncertainty quantification across multiple quantile levels.

stat.AP↗

arXiv2026

exdqlm: An R Package for Estimation and Analysis of Flexible Dynamic Quantile Linear Models

We present the R package exdqlm for Bayesian quantile regression, with primary emphasis on dynamic state-space quantile models for time series. The package is built around extended dynamic quantile linear models (exDQLMs), which use the extended asymmetric Laplace (exAL) family, a parametric extension of the asymmetric Laplace (AL) distribution commonly used in quantile regression. The software provides posterior simulation via Markov chain Monte Carlo (MCMC) and fast approximate posterior inference via Laplace-delta variational Bayes (LDVB), supporting posterior uncertainty quantification while also providing a computationally efficient option for longer time series. The same package interface supports static exAL quantile regression with regularized priors, dynamic transfer-function models for nonlinear input effects at a given quantile, post hoc posterior-predictive synthesis across separately fitted quantiles, forecasting, and quantitative and visual diagnostics for model evaluation.

stat.ME↗