Past Event: Babuška Forum

Multilevel Bayesian Analysis of Data in the Presence of Model Inadequacy and Measurement Error

Amir Shahmoradi, ICES, Dept. of Aerospace Engineering and Engineering Mechanics

Abstract

Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (inverse problem) and prediction (forward problem) involve multiple steps of data analysis, hypothesis formation, model construction, parameter estimation, model validation, and finally prediction of the quantity of interest. This talk seeks to clarify the concepts of model inadequacy, model bias, and measurement uncertainty, and the two traditional classes of uncertainty: aleatoric vs. epistemic, as well as their relationships with each other. Starting from basic principles of probability, I build and explain a hierarchical Bayesian framework to quantitatively deal with model inadequacy and noise in data. I explain how this general approach can resolve many existing logical paradoxes that frequently appear in experimental data. As an illustrative problem, I apply this methodology to an in-vitro dataset of the growth of liver tumor cells subject to significant imaging background noise. I explain how this general approach can retrieve the unknown quantities of interest from the available noisy data without any logical inconsistencies, such as obtaining negative values for quantities that are known to be inherently positive. Finally, I discuss some recent developments in the field of stochastic integration techniques with applications to numerical computation of Bayesian evidence. Bio: Dr. Amir Shahmoradi holds a PhD in Physics from the University of Texas at Austin with special focus on Biophysical sciences and a Master of Science in the field of High Energy Astrophysics. He is currently a Peter O'Donnell fellow at Institute for Computational Engineering and Sciences, and lecturer at the Department of Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin. His current research is in the area of computational oncology, Bayesian Data Analysis methods, and stochastic optimization and integration techniques.