A Dirichlet process $\operatorname{DP}(\alpha,G_0)$ can be thought of as a distribution of distributions. I would like an object similar to a Dirichlet process, but which has support only on distributions whose mean value is some fixed and known value. Precisely, I want $\mathbb{E}_G[\theta]=\mathbb{E}_{G_0}[\theta]$ to hold whenever $G$ is sampled from this Dirichlet-process-like object.

Has anyone come across something like this, or do you see a construction?

Bonus points if other moments can be constrained, too. This is to be used in a density estimation problem where the mean value of the density must be fixed.


One approach would be to use the centered Dirichlet process described in the paper "Semiparametric Bayes hierarchical models with mean and variance constraints"


This approach uses a straightforward of the usual Dirichlet process so that the mean $E_{G}[\theta]$ and variance $V_{G}[\theta]$ can equal specified values (for all G).

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