University of Athens - Seminar lecture 16/12/2014: Change Point Inference in Dynamic Erdos-Renyi Random Graphs

Σεμινάριο Στατιστικής και Επιχειρησιακής Έρευνας.

Ομιλητής: Καθηγητής κ. Γεώργιος Μιχαηλίδης Τμήμα Στατιστικής, University
of Michigan, ΗΠΑ.

Ημερομηνία-ώρα: Τρίτη 16 Δεκεμβρίου 2014 και ώρα 13:00.

Τόπος: Αίθουσα Α32 Τμήματος Μαθηματικών Πανεπιστημίου Αθηνών.

Τίτλος: Change Point Inference in Dynamic Erdos-Renyi Random Graphs

Περίληψη:  We investigate a model of an Erdos-Renyi graph, where the edges can be in a set of finite states (e.g.present/absent). The states of each edge evolve as a Markov chain independently of the other edges, and whose parameters exhibit a change-point behavior in time. We derive the maximum likelihood estimator for the change-point and characterize its distribution. Depending on a measure of the signal-to-noise ratio present in the data, different limiting regimes emerge. Nevertheless, a unifying adaptive scheme can be used in practice that covers all cases. Finally, for appropriate choices of the parameters of the Markov kernels, the
limiting distribution of the change-point exhibits long-range dependence. The model is illustrated on synthetic, as well as real data.