- Date & Time: Jan 26, 2016 from 10:00am to 12:00pm
- Location: Building 1, Room 4214
In this work, we employ statistical and Bayesian techniques to
analyze mathematical forward models. The forward models usually arise
from phenomenological and physical phenomena and are expressed through
regression-based models or partial differential equations (PDEs)
associated with uncertain parameters and input data. One of the critical
challenges in real life applications is to estimate and quantify
uncertainties of such parameters using observations. Two main
statistical inferential approaches are considered to find estimates of
the model unknown parameters: likelihood-based methods and Bayesian
techniques, the latter providing a full probability distribution for the
parameters of interest, named the posterior distribution. In the
classical approach, bootstrap confidence intervals procedures are used
to assess the estimates variability. To generate accurate fatigue life
predictions, competing forward models are ranked according to several
classical information-based measures, such as the Akaike information
criterion (AIC). A different set of predictive information criteria,
relying on cross-validation techniques, is then used to compare the
candidate Bayesian models. We also propose a novel marginalization
method for inverse problems in linear PDEs using a hierarchical Bayesian
framework. This method accounts for uncertainties in the input data and
therefore reduces the bias error of the maximum posterior estimate.
Moreover, we generalize the marginalization technique to a sequential
framework by deriving and implementing an ensemble marginalized Kalman
filter.
https://sri-uq.kaust.edu.sa/Pages/Sawlan.aspx