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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)
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)