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SUMMARY:Convergence of Gaussian process emulators with estimated hyper-par
 ameters and applications in Bayesian inverse problems - Aretha Teckentrup\
 , University of Edinburgh
DTSTART:20200131T140000Z
DTEND:20200131T150000Z
UID:TALK135952@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:We consider hierarchical Gaussian process regression\, where h
 yper-parameters appearing in the mean and covariance structure of the Gaus
 sian process emulator are a priori unknown\, and are learnt from the data\
 , along with the posterior mean and covariance. We work in the framework o
 f empirical Bayes\, where a point estimate of the hyper-parameters is comp
 uted\, using the data\, and then used within the standard Gaussian process
  prior to posterior update. Using results from scattered data approximatio
 n\, we provide a convergence analysis of the method applied to a fixed\, u
 nknown function of interest. Finally\, we consider the use of Gaussian pro
 cess emulators to approximate the mathematical model in an inverse problem
 \, and discuss related stability properties.
LOCATION:MR12
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