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B1153
**Title: **Preferential attachment and arrival times
**Authors: **Benjamin Bloem-Reddy - University of Oxford (United Kingdom) **[presenting]**

**Abstract: **Well-known models such as the Chinese Restaurant process (CRP), the Yule-Simon process, and the Preferential Attachment model are constructed from a sequence of size-biased sampling steps. Interest in these models is due in large part to the fact that power law degree distributions emerge from a simple generative mechanism. Starting with the observation that these and other models differ only in the distribution of arrival times, a class of random graph models called $(\alpha,t)$-graphs is defined. $(\alpha,t)$-graphs admit a representation in terms of products of independent beta random variables reminiscent of the so-called stick-breaking representation of the CRP, and their limiting degree sequences give rise to a number of distributional identities. Posterior inference is straightforward, and a Gibbs sampler is used to fit some example models to data.