This work employs statistical and Bayesian techniques to analyze mathematical forward models with several sources of uncertainty. The forward models usually arise from phenomenological and physical phenomena and are expressed through regressionbased models or partial differential equations (PDEs) associated with uncertain parameters and input data. One of the critical challenges in realworld applications is to quantify uncertainties of the unknown parameters using observations. To this purpose, methods based on the likelihood function, and Bayesian techniques constitute the two main statistical inferential approaches considered here.
Two problems are studied in this thesis. The first problem is the prediction of fatigue life of metallic specimens. The second part is related to inverse problems in linear PDEs. Both problems require the inference of unknown parameters given certain measurements. We first estimate the parameters by means of the maximum likelihood approach. Next, we seek a more comprehensive Bayesian inference using analytical asymptotic approximations or computational techniques.
In the fatigue life prediction, there are several plausible probabilistic stresslifetime (SN) models. These models are calibrated given uniaxial fatigue experiments. To generate accurate fatigue life predictions, competing SN models are ranked according to several classical informationbased measures. A different set of predictive information criteria is then used to compare the candidate Bayesian models. Moreover, we propose a spatial stochastic model to generalize SN models to fatigue crack initiation in general geometries. The model is based on a spatial Poisson process with an intensity function that combines the SN curves with an averaged effective stress that is computed from the solution of the linear elasticity equations.
Date of Award  Nov 10 2018 

Original language  English (US) 

Awarding Institution   Computer, Electrical and Mathematical Science and Engineering


Supervisor  Raul Tempone (Supervisor) 

 uncertainty quantification
 inverse problems
 bayesian inference
 fatigue life prediction
 parameter estimation
 data assimilation