Convergence of Gaussian process emulators with estimated hyper-parameters and applications in Bayesian inverse problems

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• Aretha Teckentrup, University of Edinburgh
• Friday 31 January 2020, 14:00-15:00
• MR12.

If you have a question about this talk, please contact Dr Sergio Bacallado.

We consider hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process emulator are a priori unknown, and are learnt from the data, along with the posterior mean and covariance. We work in the framework of empirical Bayes, where a point estimate of the hyper-parameters is computed, using the data, and then used within the standard Gaussian process prior to posterior update. Using results from scattered data approximation, we provide a convergence analysis of the method applied to a fixed, unknown function of interest. Finally, we consider the use of Gaussian process emulators to approximate the mathematical model in an inverse problem, and discuss related stability properties.

This talk is part of the Statistics series.

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