A0778
Title: Nonparametric priors with fixed mean distributions
Authors: Antonio Lijoi - Bocconi University (Italy) [presenting]
Francesco Gaffi - University of Notre Dame (United States)
Igor Pruenster - Bocconi University (Italy)
Abstract: Linear functionals, or means, of discrete random probability measures, are natural probabilistic objects, and the investigation of their properties has a long and rich history. They appear in several areas of mathematics, including statistics, combinatorics, special functions, excursions of stochastic processes and financial mathematics, among others. Most contributions have aimed at determining their distribution starting from a fully specified random probability. The inverse problem is addressed: the identification of the base measure of a discrete random probability measure yielding a specific mean distribution. Besides its theoretical interest, this is of practical relevance to Bayesian nonparametric inference, where the law of a random probability measure acts as a prior distribution. Indeed, it is more often the case where pre-experimental information is available about a finite-dimensional projection of the data-generating distribution, such as the mean, rather than about an infinite-dimensional parameter. Results concerning the Dirichlet process, the normalized stable process and the Pitman-Yor process wil be displayed. They are further extended to nonparametric mixture models that are widely used for density estimation and clustering.
