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Scan statistics are commonly used in biology, medicine, engineering and other fields where interest is in the probability of observing clusters of events in a window at an unknown location. Due to the dependent nature of the number of events in a large number of overlapping window locations, even approximate solutions for the simplest scan statistics may… (More)
In this paper we introduce a <i>randomly</i> truncated sequential hypothesis test. Using the framework of a repeated significance test (RST), we study a sequential test with truncation time based on a random stopping time. Using the functional central limit theorem (FCLT) for a sequence of statistics, we derive a general result that can be employed in… (More)
Methods using gambling teams and martingales are developed and applied to find formulas for the expected value and the generating function of the waiting time until one observes an element of a finite collection of patterns in a sequence which is generated by a two-state first or higher order Markov chain.
We show how martingale techniques (both old and new) can be used to obtain otherwise hard-to-get information for the moments and distributions of waiting times for patterns in independent or Markov sequences. In particular, we show how these methods provide moments and distribution approximations for certain scan statistics, including about variable length… (More)
We prove that for a large class of widely used term structure models there is a simple theoretical upper bound for value of LIBOR futures prices. When this bound is compared to observed futures prices, one nevertheless finds that the theoretical bound is sometimes violated by market prices. The main consequence of this observation is that virtually all of… (More)
Sleeping-waking is a basic biological rhythm. A study of sleep in epilepsy established that changes in the EEG vary with different sleep phases. Activation of epileptic electroencephalographic phenomena was observed more frequently during NREM (non-rapid eye movement) phases; the REM, or paradoxical, sleep phase seemed to inhibit such phenomena. On this… (More)
We consider a simple model of sequential decisions made by a fusion agent that receives binary-passive reports from distributed sensors. The main result is an explicit formula for the probability of making a decision before a fixed budget is exhausted. These results depend on the relationship between a special ruin problem for a " lazy random walk " and a… (More)