Department of Mathematics Calendar
Troy Butler, University of Colorado Denver, Data Consistent Inversion: An Interactive Talk Using Jupyter Notebooks
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Statistical Bayesian inference (see e.g., [1, 2]) is the most common approach solving the SIP using both data and an assumed error model on the QoI to construct posterior distributions of model inputs and model discrepancies. We have recently developed an alternative “consistent” Bayesian solution to the SIP based on the measure-theoretic principles developed in . We refer to this approach as “Data Consistent Inversion” and prove that this approach produces a distribution that is consistent in the sense that its push-forward through the QoI map will match the distribution on the observable data, i.e., we say that this distribution is consistent with the model and the data .
Motivated by computationally expensive models, we discuss the impact of using approximate models to approximate the QoI on the construction of the push-forward of the prior density. We then outline the basic theoretical argument of convergence of the push-forward of the prior density using a generalized version of the Arzela-Ascoli theorem to prove a converse of Scheffe’s theorem and discuss rates of convergence .
 M. Kennedy and A. O’Hagan, “Bayesian calibration of computer models”, Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 63, pp. 425-464, (2001).