Bayesian inverse problems

We propose a new Bayesian nonparametric approach to Wicksell’s problem by placing a Dirichlet Process prior on the observables’ distribution. This simplifies computation via conjugacy and enables asymptotically efficient estimation through projection onto the space of square-integrable, increasing functions. The resulting Isotonized Inverse Posterior (IIP) satisfies a Bernstein–von Mises theorem with minimax variance, adapting to the true cdf’s Hölder continuity without requiring smoothness estimation.

We propose a novel Bayesian approach for nonparametric estimation in Wicksell’s problem. We deviate from the classical Bayesian …