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Center for Nonlinear Studies |
Abstract: When models are defined implicitly by systems of differential equations without a closed form solution, small local errors in finite-dimensional solution approximations can propagate into large deviations from the true underlying state trajectory. Inference for such models relies on a likelihood approximation constructed around a numerical solution, which underestimates posterior uncertainty. This talk will introduce a formalism for modeling and propagating discretization uncertainty through the Bayesian inferential framework, allowing exact inference and uncertainty quantification for discretized differential equation models. Bio: Oxana Chkrebtii is an Assistant Professor in the Department of Statistics specializing in uncertainty quantification and inference for complex systems. Her research area lies at the interface between statistics and applied mathematics. Dr. Chkrebtii's primary research focus is in relating error analysis for numerical methods to probability models of uncertainty. In particular, she has developed new ways of probabilistically characterizing discretization uncertainty associated with finite-dimensional representations of the solution of nonlinear differential equations. Moreover, her research on statistical inverse problems has led to the development of an efficient approach for likelihood-free inference for models defined on variable-dimensional parameter subspaces, as well as development of methodology for state and parameter inference for functional data described by nonlinear delay differential equations.
Host: Nathan Urban