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SUMMARY:Contributed talk: Stability estimates for the optimal experimental
  design in Bayesian inverse problems - Duc-Lam Duong (LUT University)
DTSTART:20230711T133000Z
DTEND:20230711T143000Z
UID:TALK193903@talks.cam.ac.uk
DESCRIPTION:The approximation problem in Bayesian inverse problems (BIPs) 
 has been studied intensively in the last decade. In this work\, we investi
 gate some stability properties of the expected utility function for the op
 timal experimental design in BIPs. This is the ``upstream'' problem to inv
 erse problems\, which deals with how to design the experiments to acquire 
 the data efficiently for the inference task. We provide a framework for th
 is problem in a non-parametric setting and prove a convergence rate of the
  expected utility with respect to a likelihood perturbation. This rate is 
 uniform over the design space and its sharpness in the general setting is 
 demonstrated by proving a lower bound in a special case. To make the probl
 em more concrete we proceed by considering non-linear Bayesian inverse pro
 blems with Gaussian likelihood and verify that the assumptions set out for
  the general case are satisfied and regain the stability of the expected u
 tility with respect to perturbations to the observation map. Theoretical c
 onvergence rates are demonstrated numerically in different examples. This 
 is joint work with T. Helin and R. Rojo-Garcia\, both at LUT University (F
 inland).
LOCATION:Seminar Room 1\, Newton Institute
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