Deconvolution

A novel nonparametric Bayesian approach for uncertainty quantification in the deconvolution model Z = X + Y, where the goal is to estimate the distribution of X from noisy observations. By placing a Dirichlet Process prior on the observed data and isotonizing posterior draws via the Greatest Convex Majorant, the Isotonic Inverse Posterior yields computationally fast credible sets with asymptotically correct frequentist coverage, without requiring estimation of any nuisance parameters.

We address the problem of uncertainty quantification for the deconvolution model Z = X + Y, where X and Y are nonnegative random …