#### Publication Date

Summer 7-15-2020

#### Abstract

Uncertainty Quantification (UQ) is an umbrella term referring to a broad class of methods which typically involve the combination of computational modeling, experimental data and expert knowledge to study a physical system. A parameter, in the usual statistical sense, is said to be physical if it has a meaningful interpretation with respect to the physical system. Physical parameters can be viewed as inherent properties of a physical process and have a corresponding true value. Statistical inference for physical parameters is a challenging problem in UQ due to the inadequacy of the computer model. In this thesis, we provide a comprehensive overview of the existing relevant UQ methodology. The computer model is often time consuming, proprietary or classified and therefore a cheap-to-evaluate emulator is needed. When the input space is large, Gaussian process (GP) emulation may be infeasible and the predominant local GP framework is too slow for prediction when MCMC is used for posterior sampling. We propose two modifications to this LA-GP framework which can be used to construct a cheap-to-evaluate emulator for the computer model, offering the user a simple and flexible time for memory exchange. When the field data consist of measurements across a set of experiments, it is common for a set of computer model inputs to represent measurements of a physical component, recorded with error. When this structure is present, we propose a new metric for identifying overfitting and a related regularization prior distribution. We show that these parameters lead to improved inference for compressibility parameters of tantalum. We propose an approximate Bayesian framework, referred to as modularization, which is shown to be useful for exploring dependencies between physical and nuisance parameters, with respect to the inadequacy of the computer model and the available prior information. We discuss a cross validation framework, modified to account for spatial (or temporal) structure, and show that it can aid in the construction of empirical Bayes priors for the model discrepancy. This CV framework can be coupled with modularization to assess the sensitivity of physical parameters to the discrepancy related modeling choices.

#### Degree Name

Statistics

#### Level of Degree

Doctoral

#### Department Name

Mathematics & Statistics

#### First Committee Member (Chair)

Gabriel Huerta

#### Second Committee Member

Lauren Hund

#### Third Committee Member

Ronald Christensen

#### Fourth Committee Member

Trilce Estrada

#### Project Sponsors

Sandia National Laboratories

#### Language

English

#### Keywords

Model calibration, Physical parameters, Uncertainty quantification, emulation, Bayesian

#### Document Type

Dissertation

#### Recommended Citation

Rumsey, Kellin. "Methods of Uncertainty Quantification for Physical Parameters." (2020). https://digitalrepository.unm.edu/math_etds/154

#### Included in

Applied Mathematics Commons, Computer Sciences Commons, Materials Science and Engineering Commons, Mathematics Commons, Statistics and Probability Commons