Polynomial Chaos Acceleration for the Bayesian Inference of Random Fields with Gaussian Priors and Uncertain Covariance Hyper-Parameters

Handle URI:
http://hdl.handle.net/10754/624106
Title:
Polynomial Chaos Acceleration for the Bayesian Inference of Random Fields with Gaussian Priors and Uncertain Covariance Hyper-Parameters
Authors:
Le Maitre, Olivier
Abstract:
We address model dimensionality reduction in the Bayesian inference of Gaussian fields, considering prior covariance function with unknown hyper-parameters. The Karhunen-Loeve (KL) expansion of a prior Gaussian process is traditionally derived assuming fixed covariance function with pre-assigned hyperparameter values. Thus, the modes strengths of the Karhunen-Loeve expansion inferred using available observations, as well as the resulting inferred process, dependent on the pre-assigned values for the covariance hyper-parameters. Here, we seek to infer the process and its the covariance hyper-parameters in a single Bayesian inference. To this end, the uncertainty in the hyper-parameters is treated by means of a coordinate transformation, leading to a KL-type expansion on a fixed reference basis of spatial modes, but with random coordinates conditioned on the hyper-parameters. A Polynomial Chaos (PC) expansion of the model prediction is also introduced to accelerate the Bayesian inference and the sampling of the posterior distribution with MCMC method. The PC expansion of the model prediction also rely on a coordinates transformation, enabling us to avoid expanding the dependence of the prediction with respect to the covariance hyper-parameters. We demonstrate the efficiency of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
Issue Date:
7-Jan-2015
Type:
Presentation
Additional Links:
http://mediasite.kaust.edu.sa/Mediasite/Play/628cb65349684aef99c4dcdcf739ef061d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52
Appears in Collections:
Presentations; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

Full metadata record

DC FieldValue Language
dc.contributor.authorLe Maitre, Olivieren
dc.date.accessioned2017-06-05T08:35:48Z-
dc.date.available2017-06-05T08:35:48Z-
dc.date.issued2015-01-07-
dc.identifier.urihttp://hdl.handle.net/10754/624106-
dc.description.abstractWe address model dimensionality reduction in the Bayesian inference of Gaussian fields, considering prior covariance function with unknown hyper-parameters. The Karhunen-Loeve (KL) expansion of a prior Gaussian process is traditionally derived assuming fixed covariance function with pre-assigned hyperparameter values. Thus, the modes strengths of the Karhunen-Loeve expansion inferred using available observations, as well as the resulting inferred process, dependent on the pre-assigned values for the covariance hyper-parameters. Here, we seek to infer the process and its the covariance hyper-parameters in a single Bayesian inference. To this end, the uncertainty in the hyper-parameters is treated by means of a coordinate transformation, leading to a KL-type expansion on a fixed reference basis of spatial modes, but with random coordinates conditioned on the hyper-parameters. A Polynomial Chaos (PC) expansion of the model prediction is also introduced to accelerate the Bayesian inference and the sampling of the posterior distribution with MCMC method. The PC expansion of the model prediction also rely on a coordinates transformation, enabling us to avoid expanding the dependence of the prediction with respect to the covariance hyper-parameters. We demonstrate the efficiency of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data.en
dc.relation.urlhttp://mediasite.kaust.edu.sa/Mediasite/Play/628cb65349684aef99c4dcdcf739ef061d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52en
dc.titlePolynomial Chaos Acceleration for the Bayesian Inference of Random Fields with Gaussian Priors and Uncertain Covariance Hyper-Parametersen
dc.typePresentationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 6-9, 2015en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)en
dc.conference.locationKAUSTen
kaust.authorLe Maitre, Olivieren
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