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HARRY CRANE, University of Chicago

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The Cut-and-Paste Process
09 February 2012 from 4:00 PM to 5:00 PM
201 Thomas Bldg.
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In this talk, we present the cut-and-paste process, a novel infinitely exchangeable process on the state space of partitions of the natural numbers whose sample paths differ from previously studied exchangeable coalescent (Kingman 1982; Pitman 1999) and fragmentation (Bertoin 2001) processes.  Though it evolves differently, the cut-and-paste process possesses some of the same properties as its predecessors, including a unique equilibrium measure, associated measure-valued process, a Poisson point process construction and transition probabilities which can be described in terms of Kingman's paintbox process.  A parametric subfamily is related to the Chinese restaurant process and we illustrate potential applications of this model to phylogenetic inference based on RNA/DNA sequence data.  There are some potential extensions of this model to Bayesian inference, hidden Markov models and tree-valued Markov processes which we will discuss.

We also discuss how this process and its extensions fit into the more general framework of statistical modeling of structure and dependence via combinatorial stochastic processes, e.g. random partitions, trees and networks, and the practical importance of infinite exchangeability in this context.

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