{"paper":{"title":"Rapid Approximation Prediction for Kriging","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.AP","stat.CO"],"primary_cat":"stat.ME","authors_text":"Douglas Nychka, Gregory Fasshauer, Ziyu Li","submitted_at":"2026-05-28T03:11:05Z","abstract_excerpt":"Exact Kriging and conditional simulation (CS) for uncertainty quantification are computationally infeasible for modern spatial analyses with large numbers of observations and dense prediction grids. We present a rapid approximation to the Kriging prediction step for stationary Gaussian processes for a regular prediction grid by approximating each off-grid covariance vector by a sparse linear combination of on-grid covariances within a local $L$-order neighborhood of $M = (2L)^2$ neighboring grid points. This reformulation reduces complexity from $O(N n^3)$ to $O(N \\log N + nM + M^3)$ while pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29284","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29284/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}