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Researcher: Hanne Kekkonen

In this project we study the statistical behaviour of the Bayesian solutions to inverse problems, when the measurement noise decreases or, equivalently, when the amount of data tends to infinity. This is of key importance since the consistent limit behaviour guarantees the meaningfulness of the solution. In particular we examine the frequentist properties of Bayesian uncertainty quantification. Bayesian uncertainty quantification is often computationally cheap but its objective meaning is not well understood. We want to show that the Bayesian credible sets have correct frequentist coverage in some large enough space.

Related Publications 

Bernstein-von Mises Theorems and Uncertainty Quantification for Linear Inverse Problems
M Giordano, H Kekkonen – SIAM/ASA Journal on Uncertainty Quantification (2020) 8, 342