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. / Doctor of Philosophy / A crucial theme when analyzing spatial data is that locations that are closer together are more likely to have similar output values (for example, daily precipitation totals). For a particular event, common modeling approach of spatial data is to observe data at numerous locations, and make predictions for locations that were unobserved. In this work, we extend this within-event modeling approach by additionally learning about the uncertainty across different events. Through this extension, we are able to quantify uncertainty for a particular computer model (which may be modeling tropical cyclone precipitation, for example) that does not provide any uncertainty on its own. This framework can be utilized to quantify uncertainty across a vast array of computer model outputs where more than one event or model run has been obtained. We also study how inputting different values into a computer model can influence the values it produces.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/115494 |
| Date | 22 June 2023 |
| Creators | Walsh, Stephen A. |
| Contributors | Statistics, Ferreira, Marco A. R., Zick, Stephanie E., Franck, Christopher T., Higdon, David |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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