Section: New Results

Bayesian Nonparametric models for ranked data and bipartite graphs.

In [20] , the author develops a novel Bayesian nonparametric model for random bipartite graphs. The model is based on the theory of completely random measures and is able to handle a potentially infinite number of nodes. It is shown that the model has appealing properties and in particular it may exhibit a power-law behavior. Posterior characterization, a generative process for network growth, and a simple Gibbs sampler for posterior simulation are derived. The model is shown to be well fitted to several real-world social networks.

In [21] , we develop a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the prior specified by a gamma process. We derive a posterior characterization and a simple and effective Gibbs sampler for posterior simulation. We develop a time-varying extension of our model, and apply it to the New York Times lists of weekly bestselling books.