Random Partitions and Bayesian Nonparametrics (16rit674)


(McMaster University)

(University of Torino and Collegio Carlo Alberto, Italy)


The Banff International Research Station will host the "Random Partitions and Bayesian Nonparametrics" workshop in Banff from Sunday April 17 to Sunday April 24, 2016.

Measuring abundance and random sampling are important issues for resource management in ecology and many other subjects. The study on rare or elusive species has led to the development of new tools and models in probability theory and Bayesian statistics. Exchangeable random partitions have proved to be a fundamental structure for a wide range of statistical problems in Bayesian nonparametrics. Indeed they provide natural Bayesian nonparametric models for samples from a population of individuals belonging to an infinite number of distinct types with unknown proportions. Only in recent years, new discrete random structures have been proposed as Bayesian nonparametric models for samples arising from populations with more complex compositional assumptions such as, for instance, populations which evolves in time and collections of populations sharing species. Among them, the class of coagulation and fragmentation processes, of which the Kingman's coalescent is the prototypical example, certainly stands out. The objective of our project is threefold: i) to investigate conditional, or posterior, asymptotic properties of exchangeable random partitions arising by sampling from certain classes of discrete random probability measures in Bayesian nonparametrics; ii) to introduce a comprehensive methodology for making Bayesian nonparametric (predictive) inference for the genealogical structure of the Kingman's coalescent; iii) to develop algorithms in the estimation of rare species.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).