Well-posed Bayesian inverse problem in Hellinger distance
= Well-posed Bayesian inverse problem in Hellinger distance
A Bayesian inverse problem is well posed in <Hellinger distance> when every datum determines a unique posterior and the posterior depends continuously on the data in <Hellinger distance>. Since posterior measures are dominated by the prior and squared <Hellinger distance> is at most twice <total variation distance>, total-variation well-posedness implies Hellinger well-posedness.