We propose a Bayesian method for clustering from discrete data structures that commonly arise in genetics and other applications. This method is equivariant with respect to relabelling units; unsampled units do not interfere with sampled data; and missing data do not hinder inference. Cluster inference using the posterior mode performs well on simulated and real datasets, and the posterior pred...

The estimation of a covariance matrix from an insufficient amount of data is one of the most common problems in fields as diverse as multivariate statistics, wireless communications, signal processing, biology, learning theory and finance. In a joint work of Marzetta, Tucci and Simon, a new approach to handle singular covariance matrices was suggested. The main idea was to use dimensionality re...

We discuss some aspects of infinitely exchangeable partition-valued stochastic processes. In particular, we introduce the the cut-and-paste process on the state space of partitions of the natural numbers whose sample paths differ from previously studied exchangeable coalescent (Kingman, 1982) and fragmentation (Bertoin, 2001) processes. Though it evolves differently, the cut-and-paste process p...

The main article and extended discussion point to Ewens’s sampling formula (ESF) as one of a few essential probability distributions. Arratia, Barbour and Tavaré explain the emergence of ESF by the Feller coupling and also touch on number theoretic considerations; Feng provides deeper background on diffusion processes and nonequilibrium versions of ESF; and McCullagh regales us with a story fro...