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A new class of dependent random measures which we call {\it compound randommeasures} are proposed and the use of normalized versions of these randommeasures as priors in Bayesian nonparametric mixture models is considered.Their tractability allows the properties of both compound random measures andnormalized compound random measures to be derived. In particular, we show howcompound random measures can be constructed with gamma, $\sigma$-stable andgeneralized gamma process marginals. We also derive several forms of theLaplace exponent and characterize dependence through both the L\'evy copula andcorrelation function. A slice sampler and an augmented P\'olya urn schemesampler are described for posterior inference when a normalized compound randommeasure is used as the mixing measure in a nonparametric mixture model and adata example is discussed.

Compound random measures and their use in Bayesian nonparametrics