"The Cut and Paste Process" (This Week at the Statistics Seminar)
Attention conservation notice: Only of interest if you
(1) care about combinatorial stochastic processes and their statistical
applications, and (2) will be in Pittsburgh on Wednesday afternoon.
It is only in very special weeks, when we have been very good, that we
get two seminars.
- Harry Crane, "The Cut-and-Paste Process"
- Abstract: 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 samples 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 natural
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.
- Time and place: 4--5 pm on Wednesday, 1 February 2012, in Scaife Hall 125
As always, the talk is free and open to the public.
Enigmas of Chance
Posted at January 31, 2012 18:45 | permanent link