In inverse problems, the ill‐posedness manifests itself in the form of a likelihood density whose support is wide in some directions, or more generally, along some manifolds, where no clear preference to parameter values is given. An informative prior efficiently restricts the support of the posterior density where the likelihood is non‐informative.

Level curves of scatter matrices fit to data with outliers: classical (red) and robust (blue).

Locations of fire stations in Arlington, Virginia and locations of 911 Fire/EMS calls during 2010–2015. Black points are the 10 fire stations. The colored points are the locations of the calls where points of same color are calls dispatched from the same fire station.