Suspect something fishy? How statistics can help detect it, quickly.
Aleksey S. Polunchenko, Ph.D.
State University of New York at Binghamton
Suppose you are gambling at a casino in a game where you and a dealer take turns rolling a die. Naturally, you would expect the die to be fair. However, what if at some point into the game the dealer-without you seeing-replaced the die with a look-alike unfair one, so as to steer the course of the game favorably to the casino. As the die’s appearance hasn’t changed, you would continue to gamble without suspecting anything. The obvious question is: as the game progresses, can you somehow “detect” that the die has been tampered with, and do so as promptly as possible? The time at which the die was replaced (if it was replaced) is referred to as the change-point, and it is not known.
Your “detection strategy” would clearly be sequential, and based solely on the scores observed so far. The desire to detect the change quickly makes the question a gamble on its own. On the one hand, it would be desirable to find out that the die is no longer fair as fast as possible, so as to quit the game to prevent further losses and subsequently file a lawsuit against the casino. On the other hand, if you are too trigger-happy there is a risk of stopping the game too quickly, i.e., stopping the game before the fair die was replaced with the unbalanced one, which is not desirable. How does one go about solving this problem? Statistics can help!
Statistics is a branch of mathematics concerned with rational decision-making among uncertainty. This is essential in real life, as only a well-thought-out decision can enable one to take the best action available given the circumstances. This talk’s aim is to provide a gentle introduction to the nook of statistics that deals with cases when a solution has to be worked out “on-the-go”, i.e., when time is a factor as well. Specifically, the talk will focus on the so-called quickest change-point detection problem. Also known as sequential change-point detection, the subject is about designing fastest ways to detect sudden anomalies (changes) in ongoing phenomena. One example would be the above biased die detection problem. However, there are many more, arising in a variety of domains: military, finance, quality control, communications, environment-to name a few. We will consider some of the subject’s applications, and touch upon its basic ideas.
Dr. Aleksey S. Polunchenko is an Assistant Professor in the Department of Mathematical Sciences at Binghamton University in New York. Dr. Polunchenko’s area of research is mathematical statistics and specifically studying the problem of sequential (quickest) change-point detection. He is currently focusing on the case of composite hypotheses.
