{"paper":{"title":"Coordinate Transformation and Polynomial Chaos for the Bayesian Inference of a Gaussian Process with Parametrized Prior Covariance Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.CO"],"primary_cat":"math.NA","authors_text":"Ibrahim Hoteit, Ihab Sraj, Olivier P. Le Ma\\^itre, Omar M. Knio","submitted_at":"2015-01-14T11:52:42Z","abstract_excerpt":"This paper addresses model dimensionality reduction for Bayesian inference based on prior Gaussian fields with uncertainty in the covariance function hyper-parameters. The dimensionality reduction is traditionally achieved using the Karhunen-\\Loeve expansion of a prior Gaussian process assuming covariance function with fixed hyper-parameters, despite the fact that these are uncertain in nature. The posterior distribution of the Karhunen-Lo\\`{e}ve coordinates is then inferred using available observations. The resulting inferred field is therefore dependent on the assumed hyper-parameters. Here,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03323","kind":"arxiv","version":2},"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/1501.03323/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"}