Dear all, Title: Random signed measures
Abstract: In this talk I present the theory of random signed measures and its applications to Bayesian nonparametric statistics and to sparse random graphs. In particular, I provide a necessary and sufficient condition for the extension of random signed measures, which solves a 70-year-old open problem dating back to the works of Alfred Renyi. This allows us to obtain a canonical definition of a random signed measure. Further, I present a representation of completely random signed measures (CRSMs), which extends the celebrated Kingman's representation for completely random measures (CRMs) to the real-valued case. I will also discuss some examples including the Skellam point process, which we show to be equivalent to a simple signed point process with independent increments, and the Gaussian random measure.