Harry Crane

The ubiquitous Ewens sampling formula

Ewens’s sampling formula exemplifies the harmony of mathematical theory, statistical application, and scientific discovery. The formula not only contributes to the foundations of evolutionary molecular genetics, the neutral theory of biodiversity, Bayesian nonparametrics, combinatorial stochastic processes, and inductive inference but also emerges from fundamental concepts in probability theory, algebra, and number theory. With an emphasis on its far-reaching influence throughout statistics and probability, we highlight these and many other consequences of Ewens’s seminal discovery.

Clustering from Categorical Data Sequences

The three-parameter cluster model is a combinatorial stochastic process that generates categorical response sequences by randomly perturbing a fixed clustering parameter. This clear relationship between the observed data and the underlying clustering is particularly attractive in cluster analysis, in which supervised learning is a common goal and missing data is a familiar issue. The model is well equipped for this task, as it can handle missing data, perform out-of-sample inference, and accommodate both independent and dependent data sequences. Moreover, its clustering parameter lies in the unrestricted space of partitions, so that the number of clusters need not be specified beforehand. We establish these and other theoretical properties and also demonstrate the model on datasets from epidemiology, genetics, political science, and legal studies.

RELATIVELY EXCHANGEABLE STRUCTURES

We study random relational structures that are \emph{relatively exchangeable}---that is, whose distributions are invariant under the automorphisms of a reference structure

Rejoinder: The Ubiquitous Ewens Sampling Formula

\mathfrak{M}

The probability of avoiding consecutive patterns in the Mallows distribution

. When

Lipschitz partition processes

\mathfrak{M}

Edge Exchangeable Models for Interaction Networks

has {\em trivial definable closure}, every relatively exchangeable structure satisfies a general Aldous--Hoover-type representation. If

The Impact of P-hacking on “Redefine Statistical Significance”

\mathfrak{M}

Relative exchangeability with equivalence relations

satisfies the stronger properties of {\em ultrahomogeneity} and {\em

Combinatorial Lévy processes

n