A0476
Title: Random signed measures
Authors: Riccardo Passeggeri - Imperial College London (United Kingdom) [presenting]
Abstract: Point processes and, more generally, random measures are ubiquitous in modern statistics. However, they can only take positive values, which is a severe limitation in many situations. Random signed measures are introduced, also known as real-valued random measures. In particular, an existence result is provided for random signed measures, allowing the obtainment of a canonical definition for them, and a 70-year-old open problem is solved. Further, a representation of completely random signed measures (CRSMs) is provided, which extends the celebrated Kingman's representation of completely random measures (CRMs) to the real-valued case. Specific classes of random signed measures are then presented, including the Skellam point process, which plays the role of the Poisson point process in the real-valued case, and the Gaussian random measure. These measures are used to construct a Bayesian nonparametric model and a sparse random signed graph model and to explore mean function estimation in nonparametric regression.
