Martingales of patterns
Date: 12 November 2008
Time:12:30pm - 2:00pm
Venue: 126, C N Yang Reading Room, Science Centre North Block
Speaker: Prof. LI Shuo Yen Robert, Professor of Information Engineering, Department of Information Engineering, The Chinese University of Hong Kong
Abstract: This talk presents some probability knowledge in the daily language plus elementary terms. Toss a coin repeatedly until the pattern THTH appears in a run. The average waiting time is not 16. How about another pattern of length 4, say, HTHH? Not 16 either. What are the odds when the two patterns compete against each other? Well, be ready for a big surprise when you attend this talk.
Computational biologists consider patterns over the DNA alphabet {A, T, G, C} in stead of coin tossing. Financial engineers deal with patterns of patterns of ups and downs. In ad hoc networks ofwireless communications, some protocols use binary patterns of listen/talk for node discovery.
Martingale, in layman’s term, means fair gamble. Often, commonly used tools, such as markov chains, can derive special cases of certain problems through long computation, while martingale yields the general result with almost no computation. Moreover, the general result usually offers more transparent insight. A good example is the ‘team gambling” concept that first appeared in the “Martingale of patterns paper” [Ann. Prob., 1980].
