# Existence of stick breaking representations for random measures

The Dirichlet process has a roughly size ordered representation in terms of beta random variables, called a stick-breaking representation (Sethuraman, 1994). Similar results hold for the beta process, the Hierarchical Dirichlet process (Teh et al., 2006) and the Pitman-Yor process (Ishwaran and James, 2001). Is there a necessary and sufficient condition for the existence of stick breaking representations for various random measures?

• How do you define a stick breaking representation? Is it just what you get from combining a countable sample taking independently from some distribution and combining it with a distribution on $\mathbb{N}$? – Michael Greinecker Mar 17 '18 at 19:02
• I don't think there's a rigorous definition of stick-breaking, but that's what I'm looking for, yes. – Shannon S. Mar 18 '18 at 16:24