NBEB-SSP · Nonparametric Bayes and empirical Bayes for species sampling problems: classical questions, new directions and related issues

Consider a population of individuals belonging to different species with unknown proportions. Given aninitial (observable) random sample from the population, how do we estimate the number of species in thepopulation, or the probability of discovering a new species in one additional sample, or the number ofhitherto unseen species that would be observed in additional unobservable samples? These are archetypalexamples of a broad class of statistical problems referred to as species sampling problems (SSP), namely:statistical problems in which the objects of inference are functionals involving the unknown speciesproportions and/or the species frequency counts induced by observable and unobservable samples from thepopulation. SSPs first appeared in ecology, and their importance has grown considerably in the recent yearsdriven by challenging applications in a wide range of leading scientific disciplines, e.g., biosciences andphysical sciences, engineering sciences, machine learning, theoretical computer science and informationtheory, etc.The objective of this project is the introduction and a thorough investigation of new nonparametric Bayesand empirical Bayes methods for SSPs. The proposed advances will include: i) addressing challengingmethodological open problems in classical SSPs under the nonparametric empirical Bayes framework, whichis arguably the most developed (currently most implemented by practitioners) framework do deal withclassical SSPs; fully exploiting and developing the potential of tools from mathematical analysis,combinatorial probability and Bayesian nonparametric statistics to set forth a coherent modern approach toclassical SSPs, and then investigating the interplay between this approach and its empirical counterpart;extending the scope of the above studies to more challenging SSPs, and classes of generalized SSPs, thathave emerged recently in the fields of biosciences and physical sciences, machine learning and informationtheory.