Wild posteriors in the wild

Abstract

Bayesian posterior approximation has become more accessible to practitioners than ever, thanks to modern black-box software. While these tools provide highly accurate approximations with minimal user effort, certain posterior geometries remain notoriously difficult for standard methods. As a result, research into alternative approximation techniques continues to flourish. In many papers, authors validate their new approaches by testing them on posterior shapes deemed challenging or "wild." However, these shapes are not always directly linked to real-world applications where they naturally occur. In this note, we present examples of practical applications that give rise to some commonly used benchmark posterior shapes.