Title: Series representations and iid approximations of completely random measures
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Abstract: Infinite-activity completely random measures (CRMs) have become important
building blocks of complex Bayesian nonparametric models. They have been successfully 
used in various applications such as clustering, density estimation, latent feature models,
survival analysis or network science. Popular infinite-activity CRMs 
include the (generalised) gamma process and the (stable) beta process.
However, except in some specific cases, exact simulation or scalable
inference with these models is challenging and finite-dimensional approximations
are often considered. In this work, we propose a general and unified framework to
derive both series representations and finite-dimensional approximations of CRMs.
Our framework can be seen as a generalisation of constructions based on size-biased
sampling of Poisson point process It includes as special cases several known series 
representations and finite approximations as well as novel ones. In particular, 
we show that one can get novel series representations for the generalised gamma process
and the stable beta process. We show how these construction can be used to derive novel
algorithms for posterior inference, including a generalisation of the known slice sampler
for normalised CRMs mixture models introduced by Griffin and Walker (2011). 
We also provide analysis of the truncation error.