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I want to solve (or simulate) /int f(x)G(dx) where f is a function(or phrase of x) and G is DPM(Dirichlet Process mixture prior). Muliere (1998) approximate this integral when G is DP, I dont know to approximate it when G is DPM. I can write it also

/int f dG = E_{G}(f(x)) 
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A pretty classical reference is:

Markov Chain Sampling Methods for Dirichlet Process Mixture Models - Neal

which can be adapted to calculating such integrals using MCMC.

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