Multilevel Bayesian Parameter Estimation in the Presence of Model Inadequacy and Data Uncertainty

28 Nov 2017  ·  Shahmoradi Amir ICES, UT Austin ·

Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem) involve multiple steps of data analysis, hypothesis formation, model construction, parameter estimation, model validation, and finally, the prediction of the quantity of interest... This article seeks to clarify the concepts of model inadequacy and bias, measurement uncertainty, and the two traditional classes of uncertainty: aleatoric versus epistemic, as well as their relationships with each other in the process of scientific inference. Starting from basic principles of probability, we build and explain a hierarchical Bayesian framework to quantitatively deal with model inadequacy and noise in data. The methodology can be readily applied to many common inference and prediction problems in science, engineering, and statistics. read more

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Data Analysis, Statistics and Probability Instrumentation and Methods for Astrophysics Probability Biological Physics Medical Physics