Bayesian Uncertainty Quantification while Leveraging Multiple Computer Model Runs

In the face of spatially correlated data, Gaussian process regression is a very common modeling approach. Given observational data, kriging equations will provide the best linear unbiased predictor for the mean at unobserved locations. However, when a computer model provides a complete grid of forecasted values, kriging will not apply. To develop an approach to quantify uncertainty of computer model output in this setting, we leverage information from a collection of computer model runs (e.g., historical forecast and observation pairs for tropical cyclone precipitation totals) through a Bayesian hierarchical framework. This framework allows us to combine information and account for the spatial correlation within and across computer model output. Using maximum likelihood estimates and the corresponding Hessian matrices for Gaussian process parameters, these are input to a Gibbs sampler which provides posterior distributions for parameters of interest. These samples are used to generate predictions which provide uncertainty quantification for a given computer model run (e.g., tropical cyclone precipitation forecast). We then extend this framework using deep Gaussian processes to allow for nonstationary covariance structure, applied to multiple computer model runs from a cosmology application. We also perform sensitivity analyses to understand which parameter inputs most greatly impact cosmological computer model output.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2023

Author dc:creator

• Walsh, Stephen A.

Chair dc:contributor.committeechair

• Ferreira, Marco A. R.

Committee members dc:contributor.committeemember

• Zick, Stephanie E.
• Franck, Christopher T.
• Higdon, David

• Gaussian processes
• uncertainty quantification
• Bayesian statistics
• spatial statistics
• nonstationary modeling
• meteorology
• cosmology

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:38171

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/115494