A brief note on Bayesian D-optimality criterion
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We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal experimental design problem, i.e. maximizing expected information gain, is equivalent to minimizing the log-determinant of posterior covariance operator. The discussion focuses on the finite-dimensional inverse problems. However, the presentation is kept abstract to facilitate the discussion of extensions to infinite-dimensional inverse problems.
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