Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 326 / 3 / 1 / c / Solution

The problem is a well-posed Bayesian inverse problem in total variation when a unique posterior ${\mu }^y$ exists for every $y\in Y$ and the posterior map is continuous:Thus the metric supplies the precise meaning of continuous dependence on the observed data in the Bayesian version of Hadamard well-posedness.