Аннотация:
We discuss Bayesian inverse problems in Hilbert spaces. The focus is on a fast concentration of the posterior probability around the unknown true solution as expressed in the concept of posterior contraction rates. Previous results determine posterior contraction rates based on known solution smoothness. Here we show that an oracle-type parameter choice is possible. This is done by relating the posterior contraction rate to the root mean squared estimation error. The talk is based on joint work with K. Lin and S. Lu, Fudan University, Shanghai.
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