Bayesian Methods

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David Dunson Dr. David Dunson.docx

Title: Bayesian multiscale modeling

Abstract: The Bayesian paradigm provides a useful framework for uncertainty quantification (UQ) in multiscale modeling.  For example, deterministic models of a system may not fit the data perfectly and there may be uncertainty in the parameters characterizing these models.  Bayesian emulators attempt to build flexible statistical models that can allow biases and uncertainty in parameter learning, while also providing accurate uncertainty bounds.  In this talk, I provide a quick overview of some advantages of Bayesian methods, while giving an illustration through an application to modeling of muscle contractions.  There is a rich literature on ordinary differential equation (ODE) models for muscle contractions; I consider a “mechanistic hierarchical Gaussian process” that provides a hierarchical model for muscle contraction data from multiple subjects in different groups, characterizing variability among subjects, uncertainty in parameters, and misspecification of the ODE.  In considering Bayesian approaches for UQ in more complex models, such as PDEs, there is a need for new methodology.  I hope to encourage collaborations in this direction.

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