[Todos] Seminario de Probabilidad y Estadística Matemática

[Pablo Groisman]

Seminario de Probabilidad y Estadística Matemática.

ÚLTIMO ENCUENTRO 2012: Miércoles 12 de diciembre, 12:00hs.

EXPOSITOR: Ery Arias-Castro, University of California San Diego.
TITULO: Percolation-based methods for the detection of clusters in networks
LUGAR: Instituto de Cálculo, 2do piso, Pabellón 2.

RESUMEN: We consider the task of detecting a salient cluster in a
(sensor) network, which we model as an undirected graph with a random
variable attached to each node. Motivated by recent research in
environmental statistics and the drive to compete with the reigning
scan statistic, we explore alternative methods based on the
percolative properties of the network. The first method is based on
the size of the largest connected component after removing the nodes
in the network whose value is lower than a given threshold. The second
one is the upper level set scan test introduced by Patil and Taillie
(2003). We establish their performance in an asymptotic decision
theoretic framework where the network size increases to infinity. We
make abundant use of percolation theory to derive our theoretical
results and our theory is complemented with some numerical
experiments. Joint work with Geoffrey Grimmett.

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