  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 (generalized) 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 an extension of
constructions based on size-biased sampling of Poisson point process
[Perman1992]. It includes as special cases several known series representations
as well as novel ones. In particular, we show that one can get novel series
representations for the generalized gamma process and the stable beta process.
We also provide some analysis of the truncation error.
