Push-forward Measures for Parameter Identification under Uncertainty

Abstract

Here we present novel developments for the solution of stochastic inverse problems using push-forward and pullback measures. We extend previous work that focused on quantifying parameter variability to perform parameter identification under uncertainty. The previous work focuses on the transformation of distributions using discrepancies in push-forward and observed measures in contrast to updating prior beliefs with likelihood functions. The novel developments presented here focus on the extension of this approach for identifying a single “true” parameter from the aggregation and direct use of noisy data.

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