Statistics Seminar: Georgy Sofronov -- Change-point detection in binary sequences

Change-point problems (or break point problems, disorder problems) can be considered one
of the central issues of mathematical statistics, connecting asymptotic statistical
theory and Monte Carlo methods, frequentist and Bayesian approaches, fixed and
sequential procedures.  In many real applications, observations are taken sequentially
over time, or can be ordered with respect to some other criterion.  The basic question,
therefore, is whether the data obtained are generated by one or by many different
probabilistic mechanisms.  The change-point problem arises in a wide variety of fields,
including biomedical signal processing, speech and image processing, seismology,
industry (e.g.  fault detection) and financial mathematics.  In this talk, we consider
various approaches to change-point detection in binary sequences, using Monte Carlo
simulation to find estimates of change-points as well as parameters of the process on
each segment.  We also demonstrate the methods for a realistic problem arising in
computational biology.