We are creatures of habit. When the usual state of affairs is no longer, we want to be aware of the change. (Is there global warming? Has the incidence rate of breast cancer increased? Is there a change in the volatility of the stock market?) Unfortunately, often there is no one around to tell us that things are not what they used to be, and we have to rely on a sequence of (invariably noisy) observations to discern that things are different. Intuitively, if the behavior of "recent" observations seems "abnormal", we would be prone to declare that a change is in effect. As usual, the problem is in the details: what do "recent" and "abnormal" mean in practice? Moreover, if we are trigger-happy, there will be many false alarms; if we are too hesitant, the delay between a real change and its detection may be very costly. Subject to a constraint on the rate of false alarms, what is the best average delay (between a true change and its detection) attainable? What is a good procedure?
This talk will present a short review of the changepoint problem and
some of its solutions. The early proposed methods turned out to be
optimal in the ideal case that both pre-change and post-change
distributions (of an independent sequence of observations, iid
pre-change and iid post-change) are known. More recent research
relaxed these assumptions. The talk will concentrate on a set of
scenarios where progressively less is known about the distributions of
the observations, culminating in nonparametric procedures for cases
where nothing (other than independence) is assumed about the pre- and
post- change distributions.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.